diff --git a/CMakeLists.txt b/CMakeLists.txt
index 3aa5a105..93dbe3c9 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -17,14 +17,6 @@ add_compile_definitions(STAQ_VERSION_STR="${STAQ_VERSION_STR}")
 #### staq root directory
 add_compile_definitions(PROJECT_ROOT_DIR="${PROJECT_SOURCE_DIR}")
 
-#### grid synth
-option(BUILD_GRID_SYNTH "Builds staq_grid_synth, requires GMP" OFF)
-if (${BUILD_GRID_SYNTH})
-    message(STATUS "Builds staq_grid_synth - ON")
-else ()
-    message(STATUS "Builds staq_grid_synth - OFF")
-endif ()
-
 #### Force clang to use libc++
 if (${CMAKE_CXX_COMPILER_ID} MATCHES "Clang")
     set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -stdlib=libc++")
diff --git a/examples/rz_test1.qasm b/examples/rz_test1.qasm
index 83eac25e..b9d39ccb 100644
--- a/examples/rz_test1.qasm
+++ b/examples/rz_test1.qasm
@@ -3,4 +3,4 @@ include "qelib1.inc";
 
 qreg q[2];
 
-rz(2*pi/4) q;
+rx(2*pi/4) q[0];
diff --git a/examples/rz_test2.qasm b/examples/rz_test2.qasm
index 4f710b42..f45b7afb 100644
--- a/examples/rz_test2.qasm
+++ b/examples/rz_test2.qasm
@@ -3,6 +3,6 @@ include "qelib1.inc";
 
 qreg q[2];
 
-rz(0.3) q[0];
-rx(3/10) q[0];
-ry(3*100/10/100) q[1];
+rz(-0.3) q[0];
+rz(-3/10) q[0];
+rz(9*-27/100*10/81) q[0];
diff --git a/include/grid_synth/exact_synthesis.hpp b/include/grid_synth/exact_synthesis.hpp
index db66e0de..76f66a74 100644
--- a/include/grid_synth/exact_synthesis.hpp
+++ b/include/grid_synth/exact_synthesis.hpp
@@ -39,27 +39,38 @@ namespace grid_synth {
 // 1/(sqrt(omega)).
 inline str_t check_common_cases(real_t theta, const real_t& eps) {
 
-    while (theta > real_t("2"))
-        theta = theta - real_t("2");
+    // Normalize theta to the range [0,4)
+    while (theta >= real_t("4"))
+        theta = theta - real_t("4");
     while (theta < 0)
-        theta = theta + real_t("2");
+        theta = theta + real_t("4");
+
+    // Deal with the case where theta is in [2,4)
+    str_t ret = "";
+    if (theta >= real_t("2")) {
+        theta = theta - real_t("2");
+        ret = "WWWW";
+    }
 
-    if (abs(theta - real_t("0.25")) < eps) {
-        return "T w";
+    // Check multiples of 1/4 in [0,2)
+    if (abs(theta) < eps) {
+        if (ret != "")
+            return ret;
+        return "I";
+    } else if (abs(theta - real_t("0.25")) < eps) {
+        return "Tw" + ret;
     } else if (abs(theta - real_t("0.5")) < eps) {
-        return "S W W W W W W W";
+        return "SWWWWWWW" + ret;
     } else if (abs(theta - real_t("0.75")) < eps) {
-        return "S T W W W W W W W w";
+        return "STWWWWWWWw" + ret;
     } else if (abs(theta - real_t("1")) < eps) {
-        return "S S W W W W W W";
+        return "SSWWWWWW" + ret;
     } else if (abs(theta - real_t("1.25")) < eps) {
-        return "S S T W W W W W W w";
+        return "SSTWWWWWWw" + ret;
     } else if (abs(theta - real_t("1.5")) < eps) {
-        return "S S S W W W W W";
+        return "SSSWWWWW" + ret;
     } else if (abs(theta - real_t("1.75")) < eps) {
-        return "S S S T W W W W W w";
-    } else if (abs(theta - real_t("2")) < eps) {
-        return "W W W W";
+        return "SSSTWWWWWw" + ret;
     } else {
         return "";
     }
diff --git a/include/grid_synth/grid_synth.hpp b/include/grid_synth/grid_synth.hpp
new file mode 100644
index 00000000..6409a116
--- /dev/null
+++ b/include/grid_synth/grid_synth.hpp
@@ -0,0 +1,232 @@
+/*
+ * This file is part of staq.
+ *
+ * Copyright (c) 2019 - 2023 softwareQ Inc. All rights reserved.
+ *
+ * MIT License
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to deal
+ * in the Software without restriction, including without limitation the rights
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+ * copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included in
+ * all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+#ifndef GRID_SYNTH_GRID_SYNTH_HPP_
+#define GRID_SYNTH_GRID_SYNTH_HPP_
+
+#include "exact_synthesis.hpp"
+#include "matrix.hpp"
+#include "rz_approximation.hpp"
+#include "s3_table.hpp"
+#include "types.hpp"
+
+namespace staq {
+namespace grid_synth {
+
+/* Converts a GMP float to a string suitable for hashing. */
+static str_t to_string(const mpf_class& x) {
+    mp_exp_t exp;
+    // Use base 32 to get a shorter string; truncate the string
+    // to keep only the significant figures.
+    int sig_len = mpf_get_default_prec() / 5;
+    if (x < 0)
+        ++sig_len; // account for leading minus sign
+    str_t s = x.get_str(exp, 32).substr(0, sig_len);
+    return s + str_t(" ") + std::to_string(exp);
+}
+
+/* Options passed when constructing a GridSynthesizer. */
+struct GridSynthOptions {
+    long int prec; // Precision in base 10 as a positive integer (10^p)
+    int factor_effort = MAX_ATTEMPTS_POLLARD_RHO;
+    bool check = false;
+    bool details = false;
+    bool verbose = false;
+    bool timer = false;
+};
+
+class GridSynthesizer {
+  private:
+    std::unordered_map<str_t, str_t> angle_cache_;
+    const domega_matrix_table_t S3_TABLE;
+
+    real_t eps_;
+    bool check_;
+    bool details_;
+    bool verbose_;
+    bool timer_;
+
+    long long duration_;
+    bool valid_;
+
+    /* Construct GridSynthesizer objects using the make_synthesizer
+     * factory function.
+     */
+    GridSynthesizer(domega_matrix_table_t s3_table, real_t eps, bool check,
+                    bool details, bool verbose, bool timer)
+        : angle_cache_(), S3_TABLE(std::move(s3_table)), eps_(std::move(eps)),
+          check_(check), details_(details), verbose_(verbose), timer_(timer),
+          duration_(0), valid_(true) {}
+
+  public:
+    ~GridSynthesizer() {}
+
+    double get_duration() const { return static_cast<double>(duration_) / 1e6; }
+    bool is_valid() const { return valid_; }
+
+    /*! \brief Find RZ-approximation for an angle. */
+    str_t get_op_str(const real_t& angle) {
+        if (verbose_)
+            std::cerr << "Checking common cases..."
+                      << "\n";
+        str_t common_case = check_common_cases(angle / gmpf::gmp_pi(), eps_);
+        if (common_case != "") {
+            if (details_)
+                std::cerr
+                    << "Angle is multiple of pi/4, answer is known exactly"
+                    << '\n';
+            if (check_)
+                std::cerr << "Check flag = " << 1 << '\n';
+            return common_case;
+        }
+        if (verbose_)
+            std::cerr << "No common cases found" << '\n';
+
+        RzApproximation rz_approx;
+        str_t op_str;
+        if (timer_) {
+            // If timer is enabled, don't check cache or produce debug
+            // output. Just synthesize the angle.
+            auto start = std::chrono::steady_clock::now();
+            rz_approx = find_fast_rz_approximation(
+                real_t(angle) * PI / real_t("-2"), eps_);
+            op_str = synthesize(rz_approx.matrix(), S3_TABLE);
+            auto end = std::chrono::steady_clock::now();
+            duration_ += std::chrono::duration_cast<std::chrono::microseconds>(
+                             end - start)
+                             .count();
+        } else {
+            str_t angle_str = to_string(angle);
+            if (verbose_)
+                std::cerr << "Checking local cache..." << '\n';
+            if (details_)
+                std::cerr << "Angle has string representation " << angle_str
+                          << '\n';
+            if (angle_cache_.count(angle_str)) {
+                if (verbose_ || details_)
+                    std::cerr << "Angle is found in local cache" << '\n';
+                return angle_cache_[angle_str];
+            }
+
+            if (verbose_)
+                std::cerr
+                    << "Running grid_synth to find new rz approximation..."
+                    << '\n';
+            RzApproximation rz_approx =
+                find_fast_rz_approximation(angle / real_t("-2.0"), eps_);
+            if (!rz_approx.solution_found()) {
+                std::cerr << "No approximation found for RzApproximation. "
+                             "Try changing factorization effort."
+                          << '\n';
+                exit(EXIT_FAILURE);
+            }
+            if (verbose_)
+                std::cerr << "Approximation found. Synthesizing..." << '\n';
+            op_str = synthesize(rz_approx.matrix(), S3_TABLE);
+
+            if (verbose_)
+                std::cerr << "Synthesis complete." << '\n';
+            bool good = (rz_approx.matrix() ==
+                         domega_matrix_from_str(full_simplify_str(op_str)));
+            valid_ = valid_ && good;
+            valid_ = valid_ && (rz_approx.error() < eps_);
+
+            if (check_)
+                std::cerr << "Check flag = " << good << '\n';
+            if (details_) {
+                real_t scale = gmpf::pow(SQRT2, rz_approx.matrix().k());
+                std::cerr << "angle = " << std::scientific << angle << '\n';
+                std::cerr << rz_approx.matrix();
+                std::cerr << "u decimal value = "
+                          << "("
+                          << rz_approx.matrix().u().decimal().real() / scale
+                          << ","
+                          << rz_approx.matrix().u().decimal().imag() / scale
+                          << ")" << '\n';
+                std::cerr << "t decimal value = "
+                          << "("
+                          << rz_approx.matrix().t().decimal().real() / scale
+                          << ","
+                          << rz_approx.matrix().t().decimal().imag() / scale
+                          << ")" << '\n';
+                std::cerr << "error = " << rz_approx.error() << '\n';
+                str_t simplified = full_simplify_str(op_str);
+                std::string::difference_type n =
+                    count(simplified.begin(), simplified.end(), 'T');
+                std::cerr << "T count = " << n << '\n';
+                std::cerr << "----" << '\n' << std::fixed;
+            }
+            angle_cache_[angle_str] = op_str;
+        }
+        return op_str;
+    }
+
+    friend GridSynthesizer make_synthesizer(const GridSynthOptions& opt);
+};
+
+/*! \brief Initializes a GridSynthesizer object. */
+inline GridSynthesizer make_synthesizer(const GridSynthOptions& opt) {
+    domega_matrix_table_t s3_table = load_s3_table();
+
+    real_t eps = gmpf::pow(real_t(10), -opt.prec);
+    MP_CONSTS = initialize_constants(opt.prec);
+    MAX_ATTEMPTS_POLLARD_RHO = opt.factor_effort;
+
+    if (opt.verbose) {
+        std::cerr << "Runtime Parameters" << '\n';
+        std::cerr << "------------------" << '\n';
+        std::cerr << std::setw(3 * COLW) << std::left
+                  << "TOL (Tolerance for float equality) " << std::setw(1)
+                  << ": " << std::setw(3 * COLW) << std::left << std::scientific
+                  << TOL << '\n';
+        std::cerr << std::setw(3 * COLW) << std::left
+                  << "KMIN (Minimum scaling exponent) " << std::setw(1) << ": "
+                  << std::setw(3 * COLW) << std::left << std::fixed << KMIN
+                  << '\n';
+        std::cerr << std::setw(2 * COLW) << std::left
+                  << "KMAX (Maximum scaling exponent) " << std::setw(1) << ": "
+                  << std::setw(3 * COLW) << std::left << std::fixed << KMAX
+                  << '\n';
+        std::cerr << std::setw(3 * COLW) << std::left
+                  << "MAX_ATTEMPTS_POLLARD_RHO (How hard we try to factor) "
+                  << std::setw(1) << ": " << std::setw(3 * COLW) << std::left
+                  << MAX_ATTEMPTS_POLLARD_RHO << '\n';
+        std::cerr << std::setw(3 * COLW) << std::left
+                  << "MAX_ITERATIONS_FERMAT_TEST (How hard we try to check "
+                     "primality) "
+                  << std::setw(1) << ": " << std::setw(3 * COLW) << std::left
+                  << MAX_ITERATIONS_FERMAT_TEST << '\n';
+    }
+    std::cerr << std::scientific;
+
+    return GridSynthesizer(std::move(s3_table), std::move(eps), opt.check,
+                           opt.details, opt.verbose, opt.timer);
+}
+
+} // namespace grid_synth
+} // namespace staq
+
+#endif // GRID_SYNTH_GRID_SYNTH_HPP_
diff --git a/include/grid_synth/mat_vec_2x2.hpp b/include/grid_synth/mat_vec_2x2.hpp
index 0e7f222a..fef0d740 100644
--- a/include/grid_synth/mat_vec_2x2.hpp
+++ b/include/grid_synth/mat_vec_2x2.hpp
@@ -38,7 +38,7 @@ namespace grid_synth {
 using real_t = mpf_class;
 
 template <typename T = real_t>
-struct row_vec2_t;
+class row_vec2_t;
 
 // 2x1 column vector
 template <typename T = real_t>
diff --git a/include/grid_synth/matrix.hpp b/include/grid_synth/matrix.hpp
index e9b7ca75..b62f9579 100644
--- a/include/grid_synth/matrix.hpp
+++ b/include/grid_synth/matrix.hpp
@@ -258,6 +258,10 @@ inline str_t full_simplify_str(str_t str) {
     return curr_str;
 }
 
+// ========================================================================= //
+// Note: These functions are no longer used by grid_synth.
+// ========================================================================= //
+
 // Generate the set of all unitary matrices with SDE less than three
 inline domega_matrix_table_t generate_s3_table() {
     using namespace std;
diff --git a/include/grid_synth/s3_table.hpp b/include/grid_synth/s3_table.hpp
new file mode 100644
index 00000000..ab444f4f
--- /dev/null
+++ b/include/grid_synth/s3_table.hpp
@@ -0,0 +1,7488 @@
+/*
+ * This file is part of staq.
+ *
+ * Copyright (c) 2019 - 2023 softwareQ Inc. All rights reserved.
+ *
+ * MIT License
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to deal
+ * in the Software without restriction, including without limitation the rights
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+ * copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included in
+ * all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+#ifndef GRID_SYNTH_S3_TABLE_HPP_
+#define GRID_SYNTH_S3_TABLE_HPP_
+
+#include <string>
+
+#include "matrix.hpp"
+#include "rings.hpp"
+
+namespace staq {
+namespace grid_synth {
+
+static const int S3_TABLE_SIZE = 3712;
+
+// clang-format off
+static const int S3_TABLE_KEYS[S3_TABLE_SIZE][10] = 
+   {{0,0,-1,0,-1,1,1,0,2,4},
+    {0,0,0,-1,0,-1,1,1,2,2},
+    {0,0,0,1,0,1,-1,-1,2,2},
+    {0,0,0,-1,0,-1,1,1,2,1},
+    {1,0,0,0,-1,0,-1,1,2,7},
+    {0,1,0,0,-1,-1,0,-1,2,5},
+    {0,0,1,0,1,-1,-1,0,2,3},
+    {0,-1,0,0,1,1,0,1,2,4},
+    {0,0,-1,0,-1,1,1,0,2,2},
+    {0,0,0,-1,0,-1,1,1,2,0},
+    {0,1,0,0,-1,-1,0,-1,2,4},
+    {0,0,1,0,1,-1,-1,0,2,2},
+    {0,0,1,0,1,-1,-1,0,2,1},
+    {0,0,0,1,0,1,-1,-1,2,7},
+    {-1,0,0,0,1,0,1,-1,2,5},
+    {0,-1,0,0,1,1,0,1,2,2},
+    {0,0,-1,0,-1,1,1,0,2,0},
+    {1,0,0,0,-1,0,-1,1,2,4},
+    {0,1,0,0,-1,-1,0,-1,2,2},
+    {-1,0,0,0,1,0,1,-1,2,4},
+    {0,-1,0,0,1,1,0,1,2,1},
+    {0,0,-1,0,-1,1,1,0,2,7},
+    {0,0,1,0,1,-1,-1,0,2,7},
+    {-1,0,0,0,1,0,1,-1,2,3},
+    {0,0,-1,0,-1,1,1,0,2,6},
+    {0,0,0,-1,0,-1,1,1,2,4},
+    {0,0,1,0,1,-1,-1,0,2,6},
+    {-1,0,0,0,1,0,1,-1,2,2},
+    {0,0,-1,0,-1,1,1,0,2,5},
+    {0,0,0,-1,0,-1,1,1,2,3},
+    {0,1,0,0,-1,-1,0,-1,2,7},
+    {0,0,1,0,1,-1,-1,0,2,5},
+    {0,0,0,1,0,1,-1,-1,2,3},
+    {0,0,1,0,-1,-1,1,0,2,0},
+    {0,0,0,1,0,-1,-1,1,2,6},
+    {0,1,0,0,-1,1,0,1,2,1},
+    {0,0,0,1,0,-1,-1,1,2,5},
+    {0,-1,0,0,1,-1,0,-1,2,1},
+    {1,0,0,0,1,0,1,1,2,2},
+    {0,0,1,0,-1,-1,1,0,2,6},
+    {-1,0,0,0,-1,0,-1,-1,2,2},
+    {0,-1,0,0,1,-1,0,-1,2,0},
+    {0,0,-1,0,1,1,-1,0,2,7},
+    {1,0,0,0,1,0,1,1,2,1},
+    {0,1,0,0,-1,1,0,1,2,7},
+    {-1,0,0,0,-1,0,-1,-1,2,1},
+    {0,0,-1,0,1,1,-1,0,2,5},
+    {1,0,0,0,1,0,1,1,2,0},
+    {0,1,0,0,-1,1,0,1,2,6},
+    {0,0,1,0,-1,-1,1,0,2,4},
+    {-1,0,0,0,-1,0,-1,-1,2,0},
+    {0,0,0,-1,0,1,1,-1,2,2},
+    {1,0,0,0,1,0,1,1,2,7},
+    {0,1,0,0,-1,1,0,1,2,5},
+    {0,0,1,0,-1,-1,1,0,2,3},
+    {0,0,0,1,0,-1,-1,1,2,1},
+    {0,0,-1,0,1,1,-1,0,2,3},
+    {1,0,0,0,1,0,1,1,2,6},
+    {0,0,0,-1,0,1,1,-1,2,0},
+    {1,0,0,0,1,0,1,1,2,5},
+    {0,0,0,1,0,-1,-1,1,2,7},
+    {0,-1,0,0,1,-1,0,-1,2,3},
+    {0,0,-1,0,1,1,-1,0,2,1},
+    {1,0,1,1,0,0,1,0,2,2},
+    {-1,-1,1,0,-1,0,0,0,2,6},
+    {-1,0,-1,-1,0,0,-1,0,2,2},
+    {1,-1,0,-1,0,0,0,-1,2,0},
+    {1,0,1,1,0,0,1,0,2,1},
+    {-1,-1,1,0,-1,0,0,0,2,5},
+    {0,-1,-1,1,0,-1,0,0,2,3},
+    {1,-1,0,-1,0,0,0,-1,2,7},
+    {0,1,1,-1,0,1,0,0,2,3},
+    {1,0,1,1,0,0,1,0,2,0},
+    {-1,1,0,1,0,0,0,1,2,6},
+    {-1,-1,1,0,-1,0,0,0,2,4},
+    {1,-1,0,-1,0,0,0,-1,2,6},
+    {0,1,1,-1,0,1,0,0,2,2},
+    {1,0,1,1,0,0,1,0,2,7},
+    {-1,0,-1,-1,0,0,-1,0,2,7},
+    {1,1,-1,0,1,0,0,0,2,3},
+    {0,1,1,-1,0,1,0,0,2,1},
+    {1,0,1,1,0,0,1,0,2,6},
+    {-1,-1,1,0,-1,0,0,0,2,2},
+    {-1,0,-1,-1,0,0,-1,0,2,6},
+    {-1,1,0,1,0,0,0,1,2,3},
+    {0,-1,-1,1,0,-1,0,0,2,7},
+    {1,0,1,1,0,0,1,0,2,4},
+    {-1,1,0,1,0,0,0,1,2,2},
+    {-1,0,0,0,1,0,1,-1,2,6},
+    {-1,0,-1,-1,0,0,-1,0,2,4},
+    {-1,1,0,1,0,0,0,1,2,1},
+    {-1,-1,1,0,-1,0,0,0,2,7},
+    {0,-1,-1,1,0,-1,0,0,2,5},
+    {-1,0,-1,-1,0,0,-1,0,2,3},
+    {1,1,-1,0,1,0,0,0,2,7},
+    {0,-1,1,1,0,1,0,0,2,0},
+    {0,1,-1,-1,0,-1,0,0,2,0},
+    {-1,0,-1,1,0,0,1,0,2,5},
+    {1,0,1,-1,0,0,-1,0,2,5},
+    {-1,1,1,0,1,0,0,0,2,1},
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+    {1,0,0,1,-1,-1,0,0,2,1},
+    {1,1,0,0,0,-1,1,0,2,0},
+    {0,1,-1,0,0,0,-1,-1,2,6},
+    {1,0,0,1,1,1,0,0,2,3},
+    {0,0,0,1,0,-1,1,1,2,7},
+    {0,0,-1,0,0,-1,1,1,2,3},
+    {0,0,0,-1,1,0,1,1,2,3},
+    {0,0,-1,0,0,1,-1,-1,2,2},
+    {1,0,0,0,0,-1,-1,1,2,1},
+    {0,0,-1,1,-1,0,0,1,2,5},
+    {-1,1,0,0,0,1,1,0,2,2},
+    {0,0,0,-1,0,-1,0,0,1,6},
+    {1,0,0,1,1,1,0,0,2,4},
+    {0,-1,0,0,1,0,1,1,2,7},
+    {0,0,1,-1,1,0,0,-1,2,6},
+    {0,-1,0,0,0,1,0,0,1,2},
+    {0,0,1,0,0,-1,0,0,1,6},
+    {1,-1,0,0,0,-1,-1,0,2,2},
+    {-1,0,0,-1,-1,-1,0,0,2,4},
+    {0,0,0,1,0,-1,-1,1,2,4},
+    {0,0,-1,1,-1,0,0,1,2,6},
+    {1,-1,-1,0,0,0,-1,0,2,7},
+    {1,0,0,1,1,1,0,0,2,5},
+    {-1,0,0,-1,-1,-1,0,0,2,5},
+    {-1,0,0,1,0,1,-1,0,2,6},
+    {1,0,0,1,1,1,0,0,2,6},
+    {0,-1,1,0,0,0,1,1,2,2},
+    {1,0,0,0,1,1,-1,0,2,0},
+    {-1,1,0,0,0,1,1,0,2,4},
+    {0,0,-1,0,-1,0,0,0,1,2},
+    {1,-1,0,0,0,-1,-1,0,2,4},
+    {0,0,-1,1,-1,0,0,1,2,0},
+    {-1,1,0,0,0,1,1,0,2,5},
+    {-1,0,0,0,1,1,-1,0,2,7},
+    {0,0,1,-1,1,0,0,-1,2,1},
+    {0,0,1,-1,0,1,1,0,2,1},
+    {1,-1,0,0,0,-1,-1,0,2,5},
+    {-1,0,0,-1,-1,-1,0,0,2,7},
+    {0,0,-1,1,-1,0,0,1,2,1}};
+
+static const std::string S3_TABLE_VALUES[S3_TABLE_SIZE] = 
+   {"STHSTHSSSTHSSSTWWWWWW",
+    "STHSTHSSSTHSSSTWWWWW",
+    "STHSTHSSSTHSSSTW",
+    "STHSTHSSSTHSSSWWWWW",
+    "STHSTHSSSTHSSSWWWW",
+    "STHSTHSSSTHSSSWWW",
+    "STHSTHSSSTHSSSWW",
+    "STHSTHSSSTHSSTWWWWWWW",
+    "STHSTHSSSTHSSTWWWWWW",
+    "STHSTHSSSTHSSTWWWWW",
+    "STHSTHSSSTHSSTWWW",
+    "STHSTHSSSTHSSTWW",
+    "STHSTHSSSTHSSWW",
+    "STHSTHSSSTHSSW",
+    "STHSTHSSSTHSS",
+    "STHSTHSSSTHSTWWWWWWW",
+    "STHSTHSSSTHSTWWWWWW",
+    "STHSTHSSSTHSTWWWW",
+    "STHSTHSSSTHSTWWW",
+    "STHSTHSSSTHST",
+    "STHSTHSSSTHSWWWWWWW",
+    "STHSTHSSSTHSWWWWWW",
+    "STHSTHSSSTHSWW",
+    "STHSTHSSSTHS",
+    "STHSTHSSSTHTWWWWWW",
+    "STHSTHSSSTHTWWWWW",
+    "STHSTHSSSTHTWW",
+    "STHSTHSSSTHT",
+    "STHSTHSSSTHWWWWWW",
+    "STHSTHSSSTHWWWWW",
+    "STHSTHSSSTHWWW",
+    "STHSTHSSSTHWW",
+    "STHSTHSSSTHW",
+    "STHSTHSSTHSSSTWWWWW",
+    "STHSTHSSTHSSSTWWWW",
+    "STHSTHSSTHSSSWWWWWW",
+    "STHSTHSSTHSSSWWWW",
+    "STHSTHSSTHSSSWW",
+    "STHSTHSSTHSSTWWWWWWW",
+    "STHSTHSSTHSSTWWWWW",
+    "STHSTHSSTHSSTWWW",
+    "STHSTHSSTHSSTWW",
+    "STHSTHSSTHSSSW",
+    "STHSTHSSTHSSWWWWWWW",
+    "STHSTHSSTHSSWWWWWW",
+    "STHSTHSSTHSSWWW",
+    "STHSTHSSTHSSW",
+    "STHSTHSSTHSTWWWWWWW",
+    "STHSTHSSTHSTWWWWWW",
+    "STHSTHSSTHSTWWWWW",
+    "STHSTHSSTHSTWWW",
+    "STHSTHSSTHST",
+    "STHSTHSSTHSWWWWWWW",
+    "STHSTHSSTHSWWWWWW",
+    "STHSTHSSTHSWWWWW",
+    "STHSTHSSTHSWWWW",
+    "STHSTHSSTHSW",
+    "STHSTHSSTHTWWWWWWW",
+    "STHSTHSSTHT",
+    "STHSTHSSTHWWWWWWW",
+    "STHSTHSSTHWWWW",
+    "STHSTHSSTHWW",
+    "STHSTHSSTHW",
+    "STHSTHSTHSSSTWWWWWWW",
+    "STHSTHSTHSSSTWWWWW",
+    "STHSTHSTHSSSTWWW",
+    "STHSTHSTHSSSTWW",
+    "STHSTHSTHSSSWWWWWWW",
+    "STHSTHSTHSSSWWWWW",
+    "STHSTHSTHSSSWWWW",
+    "STHSTHSTHSSSWW",
+    "STHSTHSTHSSS",
+    "STHSTHSTHSSTWWWWWWW",
+    "STHSTHSTHSSTWWWWWW",
+    "STHSTHSTHSSTWWWWW",
+    "STHSTHSTHSSTWW",
+    "STHSTHSTHSST",
+    "STHSTHSTHSSWWWWWWW",
+    "STHSTHSTHSSWWW",
+    "STHSTHSTHSSW",
+    "STHSTHSTHSS",
+    "STHSTHSTHSTWWWWWWW",
+    "STHSTHSTHSTWWWWW",
+    "STHSTHSTHSTWWW",
+    "STHSTHSTHSWWWWWW",
+    "STHSTHSTHSWWWW",
+    "STHSTHSTHTWWWWWWW",
+    "STHSTHSTHTWWWWWW",
+    "STHSTHSSSTHSST",
+    "STHSTHSTHTWWW",
+    "STHSTHSTHWWWWWW",
+    "STHSTHSTHWWWWW",
+    "STHSTHSTHWWWW",
+    "STHSTHSTHWWW",
+    "STHSTHSTHW",
+    "STHSTHTHSSSTWWWWWWW",
+    "STHSTHTHSSSTWWW",
+    "STHSTHTHSSSWWWWWW",
+    "STHSTHTHSSSWW",
+    "STHSTHTHSSS",
+    "STHSTHTHSSTWWWWWWW",
+    "STHSTHTHSSTWWWWW",
+    "STHSTHTHSSTWWW",
+    "STHSTHTHSST",
+    "STHSTHTHSSWWWWWW",
+    "STHSTHTHSSWWWWW",
+    "STHSTHTHSSWWW",
+    "STHSTHTHSS",
+    "STHSTHTHSTWWWW",
+    "STHSTHTHSWWWWWW",
+    "STHSTHTHSWWW",
+    "STHSTHTHSW",
+    "STHSTHTHTWWWWWWW",
+    "STHSTHTHTWWW",
+    "STHSTHTHTWW",
+    "STHSTHTHWWWWWW",
+    "STHSTHTHWWW",
+    "STHSTHTHWW",
+    "STHTHSSSTHSSSTWWWWWWW",
+    "STHTHSSSTHSSSTWWWWWW",
+    "STHTHSSSTHSSSTWWWWW",
+    "STHTHSSSTHSSSTWWW",
+    "STHTHSSSTHSSSTW",
+    "STHTHSSSTHSSSWWWWWWW",
+    "STHTHSSSTHSSSWWW",
+    "STHTHSSSTHSSSWW",
+    "STHTHSSSTHSSTWWWWWW",
+    "STHTHSSSTHSSTWWW",
+    "STHTHSSSTHSSTWW",
+    "STHTHSSSTHSSTW",
+    "STHTHSSSTHSSWWWW",
+    "STHTHSSSTHSSWWW",
+    "STHTHSSSTHSSWW",
+    "STHTHSSSTHSTWWWWWW",
+    "STHTHSSSTHSTWWWWW",
+    "STHTHSSSTHSTWWWW",
+    "STHTHSSSTHSTWWW",
+    "STHTHSSSTHSWWWWWW",
+    "STHTHSSSTHSWWWW",
+    "STHTHSSSTHSW",
+    "STHTHSSSTHS",
+    "STHTHSSSTHTWWWWWWW",
+    "STHTHSSSTHTWWWWWW",
+    "STHTHSSSTHTWWWWW",
+    "STHTHSSSTHTWW",
+    "STHTHSSSTHTW",
+    "STHTHSSSTHT",
+    "STHTHSSSTHWWWWWW",
+    "STHTHSSSTHWWWWW",
+    "STHTHSSSTHWWWW",
+    "STHTHSSSTHWWW",
+    "STHTHSSSTHWW",
+    "STHTHSSSTH",
+    "STHTHSSTHSSSTWWWWW",
+    "STHTHSSTHSSST",
+    "STHTHSSTHSSSWWWWWW",
+    "STHTHSSTHSSSWWWWW",
+    "STHTHSSTHSSSWWWW",
+    "STHTHSSTHSSSWW",
+    "STHTHSSTHSSSW",
+    "STHTHSSTHSSS",
+    "STHTHSSTHSSTWWWW",
+    "STHTHSSTHSSTWWW",
+    "STHTHSSTHSSTWW",
+    "STHTHSSTHSSTW",
+    "STHTHSSTHSST",
+    "STHTHSSTHSSWWWWWW",
+    "STHTHSSTHSSWWWWW",
+    "STHTHSSTHSSW",
+    "STHTHSSTHSS",
+    "STHTHSSTHSTWWWWWW",
+    "STHTHSSTHSTWWWWW",
+    "STHTHSSTHSTWWW",
+    "STHTHSSTHSTWW",
+    "STHSTHSSSTHWWWWWWW",
+    "STHTHSSTHSTW",
+    "STHTHSSTHSWWWWWWW",
+    "STHTHSSTHSWWWWWW",
+    "STHTHSSTHSWWWWW",
+    "STHTHSSTHSWWWW",
+    "STHTHSSTHSWW",
+    "STHTHSSTHTWWW",
+    "STHTHSSTHTWW",
+    "STHSTHSSTHSSSTW",
+    "STHTHSSTHT",
+    "STHTHSSTHWWWWWWW",
+    "STHTHSSTHWWWW",
+    "STHTHSSTHWW",
+    "STHTHSSTHW",
+    "STHTHSSTH",
+    "STHTHSTHSSSTWWWWWW",
+    "STHTHSTHSSSTWWWW",
+    "STHTHSTHSSSTWWW",
+    "STHTHSTHSSSTWW",
+    "STHTHSTHSSSTW",
+    "STHTHSTHSSSWWWWWWW",
+    "STHTHSTHSSSWWWWW",
+    "STHTHSTHSSSWWWW",
+    "STHTHSTHSSSW",
+    "STHTHSTHSSTWWWWW",
+    "STHTHSTHSSTWW",
+    "STHTHSTHSST",
+    "STHTHSTHSSWWW",
+    "STHTHSTHSSWW",
+    "STHTHSTHSTWWWWWWW",
+    "STHSTHSSTHSSST",
+    "STHTHSTHSTWWWW",
+    "STHSTHSSTHSSSTWWWWWWW",
+    "STHTHSTHSTWW",
+    "STHTHSTHST",
+    "STHTHSTHSWWWWWWW",
+    "STHTHSTHSWWW",
+    "STHTHSTHSWW",
+    "STHTHSTHS",
+    "STHTHSTHTWWWWWW",
+    "STHTHSSSTHWWWWWWW",
+    "STHTHSTHTWWWWW",
+    "STHTHSTHTWW",
+    "STHTHSTHWWWWWWW",
+    "STHTHSTHWWW",
+    "STHTHSTHWW",
+    "STHTHSTHW",
+    "STHTHSTHSWWWW",
+    "STHTHTHSSSTWWWW",
+    "STHTHTHSSSTWW",
+    "STHTHTHSSST",
+    "STHTHTHSSSWWWWWW",
+    "STHTHTHSSSWWWWW",
+    "STHTHTHSSSWWWW",
+    "STHTHTHSSSWW",
+    "STHTHSSSTHSSSWWWWW",
+    "STHTHTHSSSW",
+    "STHTHTHSSTWWWWWWW",
+    "STHTHTHSSTWWW",
+    "STHTHTHSSWWWWWWW",
+    "STHTHTHSSWWWWWW",
+    "STHTHTHSSWWWWW",
+    "STHTHTHSSWWWW",
+    "STHTHTHSSWW",
+    "STHTHTHSTWWWWWWW",
+    "STHTHTHSTWWWWWW",
+    "STHTHTHSTWWWW",
+    "STHTHTHSTW",
+    "STHTHTHSWWWWWWW",
+    "STHTHTHSWWWWW",
+    "STHTHTHSWWWW",
+    "STHTHTHSWWW",
+    "STHTHTHS",
+    "STHTHTHTWWWWWWW",
+    "STHTHTHTWWWWWW",
+    "STHTHTHTWWWW",
+    "STHTHTHTWWW",
+    "STHTHTHT",
+    "STHTHTHWWWWWWW",
+    "STHTHTHWWW",
+    "STHTHTHW",
+    "SHSTHSSSTHSSSTWWWWWWW",
+    "SHSTHSSSTHSSSTWWW",
+    "STHSTHTHSTWWWWWW",
+    "SHSTHSSSTHSSSTWW",
+    "SHSTHSSSTHSSSTW",
+    "SHSTHSSSTHSSSWWWWWWW",
+    "SHSTHSSSTHSSSWWWWWW",
+    "SHSTHSSSTHSSSWWW",
+    "SHSTHSSSTHSSS",
+    "STHSTHTHSSSWWWW",
+    "SHSTHSSSTHSSTWWWWWWW",
+    "SHSTHSSSTHSSTWWWWWW",
+    "SHSTHSSSTHSSTWWWWW",
+    "STHSTHSSTHTWWWWWW",
+    "SHSTHSSSTHSSTW",
+    "SHSTHSSSTHSST",
+    "STHSTHSSSTHSWWW",
+    "SHSTHSSSTHSSWWWWWW",
+    "SHSTHSSSTHSSWWWWW",
+    "SHSTHSSSTHSSWWW",
+    "STHSTHSSTHSSSWWW",
+    "SHSTHSSSTHSTWWWWWWW",
+    "SHSTHSSSTHSTWWWW",
+    "SHSTHSSSTHSTWWW",
+    "SHSTHSSSTHSWWWWWW",
+    "SHSTHSSSTHSWWWW",
+    "SHSTHSSSTHSWW",
+    "SHSTHSSSTHTWWWWW",
+    "SHSTHSSSTHTWW",
+    "SHSTHSSSTHSSSW",
+    "SHSTHSSSTHT",
+    "SHSTHSSSTHWWWWWWW",
+    "SHSTHSSSTHWWWWWW",
+    "SHSTHSSSTHWWWWW",
+    "SHSTHSSSTHWWWW",
+    "SHSTHSSSTHWW",
+    "SHSTHSSTHSSSTWWWWW",
+    "SHSTHSSTHSSSTWWWW",
+    "SHSTHSSTHSSSTWWW",
+    "SHSTHSSTHSSST",
+    "SHSTHSSTHSSSWWWWWW",
+    "SHSTHSSTHSSSWWWW",
+    "SHSTHSSTHSSSWWW",
+    "SHSTHSSTHSSSWW",
+    "SHSTHSSTHSSS",
+    "SHSTHSSTHSSTWWWWWW",
+    "SHSTHSSTHSSTWWWWW",
+    "STHTHSTHT",
+    "SHSTHSSTHSSTWWWW",
+    "SHSTHSSTHSSTW",
+    "SHSTHSSTHSSWWWWW",
+    "SHSTHSSTHSSWWW",
+    "SHSTHSSTHSSWW",
+    "SHSTHSSTHSSW",
+    "SHSTHSSTHSS",
+    "STHSTHSSTHSSSTWW",
+    "SHSTHSSTHSTWWWWWWW",
+    "SHSTHSSTHSTWWWWW",
+    "SHSTHSSTHSTWWWW",
+    "SHSTHSSTHSTWWW",
+    "SHSTHSSTHSTWW",
+    "SHSTHSSTHSWWWWWW",
+    "SHSTHSSTHSWWWWW",
+    "SHSTHSSTHSWW",
+    "STHTHSSSTHSSTWWWW",
+    "SHSTHSSTHSW",
+    "SHSTHSSTHS",
+    "SHSTHSSTHSSSWWWWWWW",
+    "SHSTHSSTHTWWWW",
+    "SHSTHSSTHTWWW",
+    "SHSTHSSTHTWW",
+    "SHSTHSSTHTW",
+    "SHSTHSSTHT",
+    "SHSTHSSTHWWWWWW",
+    "SHSTHSSTHWWWWW",
+    "SHSTHSSTHWWWW",
+    "STHSTHSSTHTW",
+    "SHSTHSSTHWWW",
+    "SHSTHSSTH",
+    "SHSTHSTHSSSTWWWWWW",
+    "SHSTHSTHSSSTWWWWW",
+    "SHSTHSTHSSSTWWWW",
+    "SHSTHSTHSSSTWW",
+    "SHSTHSTHSSST",
+    "SHSTHSTHSSSWWWWWWW",
+    "SHSTHSTHSSSWWWWW",
+    "SHSTHSTHSSSWWWW",
+    "STHSTHSSSTHSTWWWWW",
+    "SHSTHSTHSSSWWW",
+    "STHSTHTHWWWWW",
+    "SHSTHSTHSSSWW",
+    "SHSTHSTHSSS",
+    "STHSTHSSSTHSSWWWW",
+    "SHSTHSTHSSTWWWWWWW",
+    "SHSTHSTHSSTWWWWW",
+    "SHSTHSTHSSTWWWW",
+    "SHSTHSTHSSTWWW",
+    "SHSTHSTHSSTWW",
+    "SHSTHSTHSST",
+    "SHSTHSTHSSWWWWWWW",
+    "SHSTHSTHSSWWWW",
+    "SHSTHSTHSSWW",
+    "SHSTHSTHSSW",
+    "SHSTHSTHSS",
+    "SHSTHSTHSTWWWWWWW",
+    "SHSTHSTHSTWWW",
+    "STHTHSTHSSST",
+    "SHSTHSTHSTWW",
+    "SHSTHSTHSTW",
+    "STHSTHTHWWWWWWW",
+    "SHSTHSTHST",
+    "SHSTHSTHSWWWWWW",
+    "SHSTHSTHSWWWWW",
+    "SHSTHSTHSWWW",
+    "SHSTHSSSTHSSSWWWWW",
+    "SHSTHSTHSWW",
+    "SHSTHSTHS",
+    "STHSTHTHSSTWWWW",
+    "SHSTHSTHTWWWWWWW",
+    "STHTHTHSSTWWWW",
+    "SHSTHSTHTWWW",
+    "SHSTHSTHWWWWWWW",
+    "SHSTHSTHWWWW",
+    "SHSTHTHSSSTWWWWWWW",
+    "SHSTHTHSSSTWWWWW",
+    "SHSTHTHSSSTWWWW",
+    "SHSTHTHSSSWWWWWW",
+    "SHSTHTHSSSWWWWW",
+    "SHSTHTHSSSWW",
+    "STHTHSSSTHSSWWWWWW",
+    "SHSTHTHSSSW",
+    "SHSTHTHSSTWWWW",
+    "SHSTHTHSSTWWW",
+    "SHSTHTHSSTWW",
+    "SHSTHTHSST",
+    "SHSTHTHSSWWWWWW",
+    "SHSTHTHSSWWWWW",
+    "SHSTHTHSSWWWW",
+    "SHSTHTHSSWWW",
+    "STHTHSSTHSSWW",
+    "SHSTHTHSS",
+    "SHSTHTHSTWWW",
+    "SHSTHSSSTHTWWWWWWW",
+    "SHSTHTHSTWW",
+    "STHTHSTHTWWWW",
+    "SHSTHTHSTW",
+    "SHSTHTHST",
+    "SHSTHTHSWWWWWWW",
+    "SHSTHTHSWWWWWW",
+    "SHSTHTHSWWWWW",
+    "SHSTHTHSWWWW",
+    "SHSTHTHSWWW",
+    "SHSTHTHSW",
+    "SHSTHTHS",
+    "SHSTHTHTWWWWWW",
+    "SHSTHTHTWWWWW",
+    "SHSTHTHTWWWW",
+    "SHSTHTHTWW",
+    "SHSTHTHT",
+    "STHTHSTHSSSTWWWWW",
+    "SHSTHTHWWWWWW",
+    "SHSTHTHWWWW",
+    "SHTHSSSTHSSSTWWWWWW",
+    "SHTHSSSTHSSSTWWWWW",
+    "SHTHSSSTHSSSTWWW",
+    "SHTHSSSTHSSST",
+    "SHTHSSSTHSSSWWWWWW",
+    "SHTHSSSTHSSSWWWW",
+    "SHTHSSSTHSSSWWW",
+    "SHTHSSSTHSSSW",
+    "SHTHSSSTHSSS",
+    "SHTHSSSTHSSTWWWWWWW",
+    "SHTHSSSTHSSTWWWW",
+    "SHTHSSSTHSSTWWW",
+    "SHTHSSSTHSSTWW",
+    "SHTHSSSTHSSTW",
+    "SHTHSSSTHSSWWWWWW",
+    "SHTHSSSTHSSWW",
+    "SHTHSSSTHSSW",
+    "SHSTHSSTHSWWWW",
+    "SHTHSSSTHSTWWWWWWW",
+    "SHTHSSSTHSTWWWWWW",
+    "SHTHSSSTHSTWWWWW",
+    "SHTHSSSTHSTWWWW",
+    "SHSTHSSSTHSSSWWWW",
+    "SHTHSSSTHSTWWW",
+    "SHTHSSSTHST",
+    "SHTHSSSTHSWWWWWWW",
+    "SHTHSSSTHSWWWWW",
+    "SHTHSSSTHSWWWW",
+    "SHTHSSSTHSWWW",
+    "SHTHSSSTHSW",
+    "SHTHSSSTHTWWWWWWW",
+    "SHTHSSSTHTWWWWWW",
+    "SHTHSSSTHTWWWW",
+    "SHTHSSSTHTWWW",
+    "SHTHSSSTHTW",
+    "SHTHSSSTHT",
+    "SHTHSSSTHWWWWWWW",
+    "SHTHSSSTHWWW",
+    "SHTHSSSTHWW",
+    "SHSTHSSSTHST",
+    "SHTHSSSTHW",
+    "SHTHSSSTH",
+    "SHTHSSTHSSSTWWWW",
+    "SHTHSSTHSSSTWWW",
+    "SHTHSSTHSSST",
+    "SHTHSSTHSSSWWWWWWW",
+    "SHTHSSTHSSSWWWWWW",
+    "SHTHSSTHSSSWWWWW",
+    "SHTHSSTHSSSWWW",
+    "SHTHSSTHSSSWW",
+    "SHTHSSTHSSSW",
+    "SHTHSSTHSSTWWWWWW",
+    "SHTHSSTHSSTWWW",
+    "SHTHSSTHSSTWW",
+    "SHSTHSSTHTWWWWW",
+    "SHTHSSTHSSWWWWWWW",
+    "SHTHSSTHSSWWWWWW",
+    "SHTHSSTHSSWWWWW",
+    "SHTHSSTHSSWWWW",
+    "SHTHSSTHSSWWW",
+    "SHTHSSTHSSW",
+    "SHTHSSTHSTWWWWWW",
+    "SHTHSSTHSTWWWWW",
+    "SHTHSSTHSTWWWW",
+    "STHTHTHSSSTWWWWWW",
+    "SHTHSSTHSTWWW",
+    "SHTHSSTHSTWW",
+    "SHTHSSTHSTW",
+    "SHTHSSTHST",
+    "SHTHSSTHSWWWWWWW",
+    "SHTHSSTHSWWWWWW",
+    "SHTHSSTHSWWWWW",
+    "SHTHSSTHSWWWW",
+    "SHTHSSTHSWWW",
+    "SHTHSSTHSWW",
+    "SHTHSSTHSW",
+    "SHTHSSTHS",
+    "SHTHSSTHTWWWWW",
+    "SHTHSSTHTWWWW",
+    "SHTHSSTHTW",
+    "SHTHSSTHT",
+    "SHTHSSTHWWWWWWW",
+    "SHTHSSTHWWWWWW",
+    "SHTHSSTHWWWWW",
+    "SHTHSSTHWWWW",
+    "SHTHSSTHWWW",
+    "SHTHSSSTHSS",
+    "SHTHSSTHWW",
+    "SHTHSSTHW",
+    "SHTHSSTH",
+    "SHTHSTHSSSTWWWWWWW",
+    "SHSTHSSSTHSTWWWWW",
+    "SHTHSTHSSSTWWWWW",
+    "SHTHSTHSSSTWWWW",
+    "SHTHSTHSSST",
+    "SHTHSTHSSSWWWWWW",
+    "SHTHSTHSSSWWWWW",
+    "SHTHSTHSSSWWW",
+    "STHSTHSTHSWWWWW",
+    "SHTHSTHSSTWWWWWWW",
+    "SHSTHSTHSTWWWW",
+    "SHTHSTHSSTWWWWW",
+    "SHTHSTHSSTWWWW",
+    "SHTHSTHSSTW",
+    "SHTHSTHSST",
+    "SHTHSTHSSWWWWW",
+    "SHTHSTHSSWWWW",
+    "SHTHSTHSSWWW",
+    "SHTHSTHSTWWWWWWW",
+    "SHTHSTHSTWWWWW",
+    "SHTHSTHSTWWWW",
+    "SHSTHSTHWWWWW",
+    "SHTHSTHSTW",
+    "SHTHSTHSWWWWWW",
+    "SHTHSTHSWWWWW",
+    "SHTHSTHSW",
+    "SHTHSTHTWWWWWWW",
+    "SHTHSTHTWWWWW",
+    "SHTHSTHTWWWW",
+    "SHSTHSSSTHSWWW",
+    "SHTHSTHTWW",
+    "SHTHSTHT",
+    "SHTHSTHWWWWW",
+    "SHTHSTHWWWW",
+    "SHTHSTHWWW",
+    "STHSTHTHSSTW",
+    "SHTHSTHWW",
+    "SHTHSTHW",
+    "SHTHTHSSSTWWWWWWW",
+    "SHTHTHSSSTWWWW",
+    "SHTHSSSTHSST",
+    "SHTHTHSSSTWWW",
+    "SHTHTHSSSTWW",
+    "SHTHTHSSSTW",
+    "SHTHTHSSST",
+    "SHTHTHSSSWWWWWW",
+    "SHTHTHSSSWWWWW",
+    "SHTHSSTHSSTW",
+    "SHTHTHSSSWWWW",
+    "STHTHSSTHSSWWWW",
+    "SHTHTHSSSWW",
+    "SHTHTHSSSW",
+    "SHTHTHSSS",
+    "SHTHTHSSTWWWWWW",
+    "SHTHTHSSTWWWW",
+    "STHTHSSSTHSWWWWW",
+    "SHTHTHSSTWW",
+    "SHTHTHSSTW",
+    "SHTHTHSST",
+    "SHTHTHSSWWWWW",
+    "SHTHTHSSWW",
+    "SHTHSSSTHSSTWWWWW",
+    "SHTHSTHSS",
+    "SHTHTHSS",
+    "SHTHTHSTWWWWW",
+    "SHTHTHSTWWWW",
+    "SHTHTHSTWW",
+    "SHTHTHSTW",
+    "SHTHTHSWWWW",
+    "STHSTHTHST",
+    "SHTHTHSWWW",
+    "SHTHTHSWW",
+    "SHTHTHSW",
+    "SHTHTHTWWWWWWW",
+    "SHTHTHTWWWWW",
+    "SHTHTHTWWWW",
+    "SHTHTHTW",
+    "SHTHTHWWWWWWW",
+    "SHTHTHWWWWWW",
+    "SHTHTHWWWW",
+    "STHSTHSTHSW",
+    "SHTHTHWW",
+    "SHTHTHW",
+    "THSTHSSSTHSSSTWWWWWW",
+    "THSTHSSSTHSSSTWWWWW",
+    "THSTHSSSTHSSSTW",
+    "THSTHSSSTHSSST",
+    "THSTHSSSTHSSSWWWWWW",
+    "THSTHSSSTHSSSWWWWW",
+    "THSTHSSSTHSSSWW",
+    "STHSTHSTHSSWWWWW",
+    "THSTHSSSTHSSTWWWWWWW",
+    "THSTHSSSTHSSTWWWWWW",
+    "STHTHTHSW",
+    "THSTHSSSTHSSTWWW",
+    "THSTHSSSTHSSTWW",
+    "STHSTHSTHSWWW",
+    "THSTHSSSTHSST",
+    "SHSTHSSTHSSSTWWWWWWW",
+    "SHTHTHST",
+    "THSTHSSSTHSSWWWW",
+    "THSTHSSSTHSTWWWWWW",
+    "THSTHSSSTHSTWWWWW",
+    "THSTHSSSTHSTWW",
+    "THSTHSSSTHST",
+    "THSTHSSSTHSWWWWWWW",
+    "THSTHSSSTHS",
+    "THSTHSSSTHTWWWW",
+    "THSTHSSSTHTWWW",
+    "STHSTHSSTHSSWWWW",
+    "THSTHSSSTHTWW",
+    "STHSTHSSTHTWWW",
+    "THSTHSSSTHTW",
+    "THSTHSSSTHT",
+    "THSTHSSSTHWWWWWWW",
+    "THSTHSSSTHWWWWWW",
+    "STHSTHSSSTHSWWWWW",
+    "THSTHSSSTHSWWW",
+    "THSTHSSSTHWWWW",
+    "THSTHSSSTHWW",
+    "THSTHSSSTHW",
+    "THSTHSSSHSSSTWWWWWWW",
+    "STHSTHSSTHTWWWWW",
+    "THSTHSSSHSSSTWWWW",
+    "THSTHSSSHSSSTWWW",
+    "THSTHSSSTHSSW",
+    "THSTHSSSHSSSTWW",
+    "THSTHSSSHSSSTW",
+    "SHTHTHSSWWW",
+    "THSTHSSSHSSSWWWWWWW",
+    "THSTHSSSHSSSWWWWWW",
+    "THSTHSSSHSSSWWWWW",
+    "THSTHSSSHSSSWWWW",
+    "THSTHSSSHSSSWWW",
+    "THSTHSSSHSSSWW",
+    "THSTHSSSHSSSW",
+    "STHTHTHSWW",
+    "THSTHSSSHSSS",
+    "THSTHSSSHSSTWWWWWWW",
+    "THSTHSSSHSSTWWWWWW",
+    "THSTHSSSTHSS",
+    "THSTHSSSHSSTWWWWW",
+    "THSTHSSSHSSTWWWW",
+    "STHTHSTHSSSTWWWWWWW",
+    "THSTHSSSHSSTWWW",
+    "THSTHSSSHSSTW",
+    "THSTHSSSHSSWWWWWW",
+    "THSTHSSSHSSWW",
+    "STHSTHSTHSSSTWWWWWW",
+    "SHSTHSSSTHTW",
+    "THSTHSSSHSS",
+    "THSTHSSSHSTWWWWWWW",
+    "SHTHSTHSSSTWW",
+    "THSTHSSSHSTWWWWWW",
+    "STHTHSSTHTWWWWWW",
+    "THSTHSSSHSTWWWWW",
+    "THSTHSSSHSTWWWW",
+    "THSTHSSSHSTWWW",
+    "THSTHSSSHSTW",
+    "THSTHSSSHST",
+    "THSTHSSSHSWWWWWW",
+    "THSTHSSSHSWWWW",
+    "THSTHSSSHSWW",
+    "THSTHSSSHTWWWWWWW",
+    "SHSTHTHTWWWWWWW",
+    "THSTHSSSHTWWWWWW",
+    "THSTHSSSHTWWWW",
+    "THSTHSSSHTWW",
+    "SHSTHTHSTWWWW",
+    "THSTHSSSHWWWWWWW",
+    "SHSTHSTHSSTWWWWWW",
+    "THSTHSSSHWWWWWW",
+    "THSTHSSSHWWWWW",
+    "THSTHSSSHWW",
+    "THSTHSSSHW",
+    "THSTHSSSH",
+    "THSTHSSTHSSSTWWWWWWW",
+    "THSTHSSTHSSSTWWWWWW",
+    "THSTHSSTHSSSTWWWWW",
+    "THSTHSSTHSSSTWWWW",
+    "THSTHSSTHSSSTWWW",
+    "THSTHSSTHSSSTWW",
+    "THSTHSSTHSSST",
+    "STHSTHSSTHSWW",
+    "SHTHTHT",
+    "THSTHSSTHSSSWWWWWWW",
+    "THSTHSSTHSSSWWWWW",
+    "THSTHSSTHSSSWWWW",
+    "THSTHSSTHSSSW",
+    "THSTHSSTHSSS",
+    "SHTHTHSWWWWWWW",
+    "THSTHSSTHSSTWWWW",
+    "STHSTHSSTHSS",
+    "THSTHSSTHSSTWW",
+    "THSTHSSTHSSTW",
+    "SHSTHSTHSWWWW",
+    "THSTHSSTHSST",
+    "THSTHSSTHSSWWWWWWW",
+    "STHTHSTHWWWW",
+    "THSTHSSTHSSWWWWWW",
+    "STHTHTHTWW",
+    "THSTHSSTHSSWW",
+    "THSTHSSTHSS",
+    "THSTHSSTHSTWWWWWWW",
+    "THSTHSSTHSTWWWWWW",
+    "STHSTHSSTHSTW",
+    "STHTHSSSTHW",
+    "THSTHSSTHSTWWWWW",
+    "THSTHSSTHSTWWW",
+    "STHTHSSSTHSSTWWWWW",
+    "SHSTHSTHSTWWWWWW",
+    "THSTHSSTHSTWW",
+    "THSTHSSTHSTW",
+    "THSTHSSTHST",
+    "THSTHSSTHSWWWWW",
+    "THSTHSSTHSWW",
+    "THSTHSSTHSW",
+    "STHSTHTHSWWWWWWW",
+    "SHTHSTHSSSW",
+    "THSTHSSTHS",
+    "THSTHSSTHTWWWWWWW",
+    "THSTHSSTHTWWWWWW",
+    "THSTHSSTHTWWWW",
+    "THSTHSSTHTWWW",
+    "THSTHSSTHTWW",
+    "THSTHSSTHT",
+    "STHTHSTHSSTWWWW",
+    "THSTHSSTHWWWWW",
+    "THSTHSSTHWW",
+    "THSTHSSTH",
+    "THSTHSTHSSSTWWWWWWW",
+    "THSTHSTHSSSTWWWWWW",
+    "THSTHSSSTHSSSTWW",
+    "THSTHSTHSSSTWWWW",
+    "THSTHSTHSSSTWW",
+    "THSTHSTHSSSTW",
+    "THSTHSTHSSSWWWWWW",
+    "THSTHSTHSSSWWWWW",
+    "THSTHSTHSSSWWWW",
+    "THSTHSTHSSSWW",
+    "THSTHSTHSSSW",
+    "THSTHSTHSSS",
+    "THSTHSTHSSTWWWWW",
+    "THSTHSTHSSTWW",
+    "THSTHSTHSSTW",
+    "THSTHSTHSST",
+    "THSTHSTHSSWWWWWWW",
+    "THSTHSSSHS",
+    "THSTHSTHSSWWWWW",
+    "THSTHSTHSSWWWW",
+    "STHTHTHTWWWWW",
+    "THSTHSTHSSWW",
+    "THSTHSTHSSW",
+    "THSTHSTHSS",
+    "STHSTHSTHSTWWWW",
+    "THSTHSTHSTWWWWWW",
+    "THSTHSTHSTWWW",
+    "THSTHSTHSTWW",
+    "THSTHSTHSWWWWWW",
+    "THSTHSTHSWWWWW",
+    "SHTHTHSTWWW",
+    "THSTHSTHSWWWW",
+    "THSTHSTHSWWW",
+    "THSTHSTHSWW",
+    "THSTHSTHTWWWW",
+    "THSTHSTHTWWW",
+    "THSTHSTHTW",
+    "THSTHSTHT",
+    "SHTHSSSTHTWW",
+    "THSTHSTHWWWWWW",
+    "THSTHSTHWWWWW",
+    "THSTHSTHWWWW",
+    "THSTHSTHWW",
+    "THSTHSTH",
+    "THSTHSSSTHTWWWWW",
+    "THSTHTHSSSTWWWWWWW",
+    "THSTHTHSSSTWWWWWW",
+    "STHTHTHSSSTW",
+    "THSTHTHSSSTWWW",
+    "THSTHTHSSSTWW",
+    "THSTHTHSSSTW",
+    "THSTHTHSSSWWWWWW",
+    "STHTHTHWW",
+    "THSTHTHSSSWWWWW",
+    "THSTHTHSSSWW",
+    "THSTHTHSSS",
+    "THSTHTHSSTWWWWWW",
+    "THSTHTHSSTWW",
+    "THSTHTHSSTW",
+    "THSTHTHSST",
+    "THSTHTHSSWWWWWWW",
+    "THSTHTHSSWWWWWW",
+    "SHTHSSTHSSTWWWWWWW",
+    "THSTHTHSSWWWWW",
+    "THSTHTHSSWWW",
+    "THSTHTHSSWW",
+    "THSTHTHSSW",
+    "SHSTHSSTHSWWWWWWW",
+    "THSTHTHSTWWWWWWW",
+    "STHSTHTHSTWW",
+    "THSTHTHSTWWWWWW",
+    "THSTHTHSTWWWW",
+    "THSTHTHSTWW",
+    "THSTHTHSTW",
+    "THSTHTHSWWWWWWW",
+    "THSTHTHSWWWWW",
+    "THSTHTHSWWWW",
+    "THSTHTHSWWW",
+    "THSTHTHSWW",
+    "THSTHTHS",
+    "THSTHTHTWWWWWW",
+    "THSTHTHTWWWWW",
+    "THSTHTHTWWWW",
+    "SHTHSSTHSSSTW",
+    "THSTHSSSHT",
+    "THSTHTHTWWW",
+    "THSTHTHTW",
+    "THSTHTHWWWWWWW",
+    "THSTHTHWWWWWW",
+    "THSTHTHWWWWW",
+    "THSTHTHWWW",
+    "THSTHTHWW",
+    "THSTHTHW",
+    "THSTHTH",
+    "THSHSSSTHSSSTWWWWWWW",
+    "THSHSSSTHSSSTWWWW",
+    "THSHSSSTHSSSTWWW",
+    "SHTHSSSTHSSSWW",
+    "THSHSSSTHSSSTWW",
+    "STHSTHSTHSSSTWWWW",
+    "STHSTHSTHTWW",
+    "THSHSSSTHSSST",
+    "SHTHSTHWWWWWW",
+    "THSHSSSTHSSSWWWWWW",
+    "THSHSSSTHSSSWWWWW",
+    "HSHSTHSWWWW",
+    "SHTHSTHS",
+    "THTHSHSSTWWWWWW",
+    "THSHTHSSTWWWWW",
+    "SHSTHTHTWWW",
+    "HSHSTHSWWW",
+    "HSHSSSHSSTW",
+    "HSHSTHSWW",
+    "HSHSTH",
+    "HSTHSTHSSSTWWWWW",
+    "HSHTHSSSTWWWWWW",
+    "HSHTHSSSTWWWW",
+    "STHSTHSTHTWWWW",
+    "HSHTHSSSTWWW",
+    "SHSWWWWWW",
+    "SSSHSWWW",
+    "SHTHSSSTHSSSTW",
+    "HSTHSSTHSSSW",
+    "HSHTHSSSTWW",
+    "HTHSTHSSSTWWW",
+    "HSHTHSSSTW",
+    "THSHSTHSWWWW",
+    "THTHTHS",
+    "STHSTHTHSSSWWW",
+    "HSHTHSSSWWWW",
+    "SHSTHSSTHSWWW",
+    "SSSHSSSWWWWWW",
+    "HSHTHSSTWWWWWWW",
+    "HTHSSSTHSSWWWWW",
+    "SSSTHSWW",
+    "HSHSSTHSSSTWWWW",
+    "HSHTHSSTW",
+    "HTHT",
+    "HSTHTHSWWWWWW",
+    "THSHSSTHSTWW",
+    "HSHTHSSWWWW",
+    "THSHSSSTHSSSTWWWWWW",
+    "THTHSSSHWWWWWW",
+    "HSHTHSSWW",
+    "STHSTWWWWW",
+    "HSTHSSTHTWW",
+    "HSHTHSTWWWWWW",
+    "SHTHTHSTWWWWWW",
+    "HSTHSSTHTW",
+    "HSHTHSTWWW",
+    "HSTHSSSHW",
+    "HSHTHSTW",
+    "STHSTHTH",
+    "HSHSSTHSSSWWWWW",
+    "THTHSSTHWWWW",
+    "STHTHSTHSSTWWW",
+    "HSHTHSWWWWW",
+    "HSHSTHWWW",
+    "THSTWWWWW",
+    "HSHTHTWWWWWW",
+    "STHSSWWWWW",
+    "SHSTHTH",
+    "HSHTHTWWWWW",
+    "SSTHSSTWWW",
+    "HSHTHSSSWWWWW",
+    "SHSTHSSSTHTWWWW",
+    "HSHTHTW",
+    "STHTHSTHSSWWWWWW",
+    "HSHTHWWWWWW",
+    "HTHSSSTHWWWWW",
+    "HSHTHWW",
+    "STHSTHSSTHSSWWWWW",
+    "HSHTH",
+    "HTHTHWWW",
+    "SSSHSSW",
+    "HTHSSSTHSSSTWWWW",
+    "HTHSSSTHSSSTWWW",
+    "HSSSWWWWW",
+    "STHTHSSTHSW",
+    "HTHSSSTHSSSWWWWWWW",
+    "HSTHSSTHSWWW",
+    "SHTHSTHSWWW",
+    "THTHSSW",
+    "HTHSSSTHSSSWW",
+    "HTHSWWWWW",
+    "HTHSSSTHSSS",
+    "STHTHTHSS",
+    "THSSWWWWWWW",
+    "HSHSTHT",
+    "HSHTHS",
+    "HSTHSSSHSSSWWWW",
+    "HTHSSSTHSSTWWWW",
+    "HTHSSSTHSSTW",
+    "HTHSSSTHSSTWW",
+    "HSTHSSSHSSSWWW",
+    "THSTHSTHSSST",
+    "THTHSSSTHTWWWWWW",
+    "SHTHSSSTHWWWWWW",
+    "HSHTHSSTWW",
+    "SHSTHSTHTW",
+    "SSSH",
+    "SHSTHSSTHTWWWWWW",
+    "HSHTHSST",
+    "HTHSSSTHSSWW",
+    "THTHSSTHTWWWWWW",
+    "HTHSSSTHSTWW",
+    "SSHSST",
+    "HTHSSSTHSTW",
+    "HSHTHW",
+    "HTHSSSTHSWWWWWWW",
+    "HSHSSTHSSWWWW",
+    "THTHSTHSSWWW",
+    "HSTHSSTHSW",
+    "THSHSTHWWWWWW",
+    "HTHSSSTHS",
+    "SHSTHTHSSTWWWWWWW",
+    "HTHSSTHSST",
+    "HSHSTHSSSWW",
+    "THTHSHSSTWWWWWWW",
+    "SHTHSTHSSWWWWWW",
+    "THTHSSTHSSSWWW",
+    "HTHTHSSWWW",
+    "HTHSSSTH",
+    "HSHSSTHSSTWWWW",
+    "THSHSSTHSTWWWWW",
+    "HTHSSSTWWWW",
+    "HTHSSSTWW",
+    "SHTHTHWWWWW",
+    "SHTHTHWWW",
+    "HTHSSSTW",
+    "STHSTHSSTHSTWW",
+    "THTHSTHSSTWW",
+    "HTHSSST",
+    "THSTHSTHSSTWWWW",
+    "THSTHSTHWWW",
+    "HTHSHSSWW",
+    "HTHSTHSSSWWWW",
+    "SHSTHSTHTWWWW",
+    "HTHSSSHSSSTWWWWW",
+    "SSTHWWWWW",
+    "HSTHSSSTHWWWWWWW",
+    "HTHSSSHSSSTWWWW",
+    "HSHTHTWWWW",
+    "HTHSSTHS",
+    "HTHSSSHSSSTWWW",
+    "SHTHSSTHTWW",
+    "HTHSSSHTWW",
+    "HTHSSTWW",
+    "HTHSSSHSSSTW",
+    "HSHSTHWW",
+    "HTHTHTWWWWWW",
+    "HTHSSSHSSST",
+    "HTHSSSHSSSWWWWWWW",
+    "THSHTHSSTWW",
+    "HTHSSSHSSSWWWWW",
+    "SHSTHSTH",
+    "THTHSTHWWWWWWW",
+    "HTHSSSHSSSWWW",
+    "SHTHTHSSSTWWWWW",
+    "HTHSSSHSSS",
+    "HTHSSSTHWWW",
+    "HTHSSSHSST",
+    "HSHTHT",
+    "STHTHSTH",
+    "HTHSSSHSSWWWWW",
+    "HTHSSSHSSWWW",
+    "HTHSSSHSSW",
+    "STHTHTH",
+    "HTHSSSHSTWWWWWWW",
+    "THSHSSTHTWWWWWW",
+    "HTHSSSTHW",
+    "HTHSSSHSWWW",
+    "THTHSSSTHSSTWWWWW",
+    "HTHSSSHS",
+    "HSTHSTHSSS",
+    "HTHSSSHTW",
+    "HTHSSSHT",
+    "HSHSSSTHTWWWWWWW",
+    "HSHTHSSS",
+    "SHSTHSTHSSSWWWWWW",
+    "SHSTHSTHSTWWWWW",
+    "HTHSSSHWWWWW",
+    "THSHSSTHSSSTWW",
+    "HTHSSSHWW",
+    "HTHSSSWW",
+    "HSHSSSTHWWW",
+    "HTHSSTHSSSTWWWWWW",
+    "STHSSTWWWWWWW",
+    "THSTHSSSHTWWW",
+    "THSTHSTHSW",
+    "SSTHTWWW",
+    "HSTHSTHSSTWWWWWWW",
+    "THTHSSTHSTWWW",
+    "HTHSSSTWWW",
+    "SSHSTWWWWWW",
+    "HTHSSTHSSSTWW",
+    "HTHSSTHSSST",
+    "THSTHSTHSTWWWWW",
+    "HTHSSTHSSSWWWW",
+    "TWWWW",
+    "HTHSSTHSSTWWWWWW",
+    "THSTHTHWWWW",
+    "HTHSSTHSSTWWWWW",
+    "HTHSTHSWWW",
+    "SHSTHTHSWW",
+    "T",
+    "THSHSSTHTW",
+    "STHSTHSTHSSSWWWWWW",
+    "HTHSSTHSSTWWW",
+    "STHTHSTHTW",
+    "HTHSSSHWWWWWWW",
+    "HTHSSTHSSTW",
+    "HTHSSTHSSWWWWWW",
+    "HTHSSWWWWW",
+    "THTHTHSSSWWW",
+    "STHSTHSTHTW",
+    "HTHSSTHSSWWWW",
+    "THSHSTHSTWWWWWWW",
+    "HTHSSTHSSWWW",
+    "HTHSSSHSTWW",
+    "HTHSSSTHSSWWWWWWW",
+    "STHSTHSSTHWWW",
+    "HTHSSTHSSWW",
+    "HTHSSTHSSW",
+    "HTHSSTHSTWWWW",
+    "SHTHSTHTW",
+    "THSHSTHSSSTWW",
+    "STHTHTHTW",
+    "HTHSSTHST",
+    "THSTHTHSSSTWWWW",
+    "HTHTHSTWWWW",
+    "HTHSSSHSWWWWW",
+    "HSHTHWWWW",
+    "HTHSSTHSWWWWW",
+    "SSHSSSTWWWWW",
+    "HSWWWWWW",
+    "STHSTHSSSTHTWWWWWWW",
+    "THTHSHSSST",
+    "HTHSSTHSWWWW",
+    "HTHSSTHSWW",
+    "THTHSSSTHSST",
+    "HSHSTHTWW",
+    "THSTHSTHWWWWWWW",
+    "STHSSTWWWW",
+    "THSTHSSTHSWWWWWWW",
+    "HTHTHWWWWW",
+    "HTHSSTHTWWW",
+    "HTHSSSWWWWWWW",
+    "HSHSSTHSTW",
+    "HTHSSTHTWW",
+    "HSTHSSSHSTWWWW",
+    "THTHSWW",
+    "HTHSSTHT",
+    "SHTHSSTHSSWW",
+    "SHTHSTHSWWWW",
+    "HTHSSTHWWWWWW",
+    "STHSTHSSSTHSSWWWWW",
+    "HTHSSTHWWWWW",
+    "HTHSSTHWWWW",
+    "HTHSSTHWW",
+    "SWWWWWWW",
+    "HSTHSSSHSSSTWWWWWWW",
+    "THSTHSSSHSW",
+    "HTHSSSTHT",
+    "HTHSSTWWWWWWW",
+    "HTHSSTWWWWW",
+    "HTHSSTWWWW",
+    "SHSTHSSTHTWWWWWWW",
+    "SHTHSSTHSSTWWWW",
+    "HTHSSSTHSSST",
+    "STHSTHTHSSSWWWWW",
+    "SHTHSSSTHSWW",
+    "HSHTHSSSWW",
+    "HSTHTHSSTWW",
+    "HTHSSSHSWWWWWW",
+    "HTHSSTWWW",
+    "SHSTHSSSTHS",
+    "HSTHSSSTHSSTWWWW",
+    "THTHTHTWWWWW",
+    "STHSTHTHSSW",
+    "HTHSST",
+    "THTHSSSTHSSTW",
+    "THSHSSSTHWWWWW",
+    "HTHSSWWWWWWW",
+    "THSHSSTHSSWW",
+    "HSHSTHSSTWWWWWWW",
+    "THTHSTHSSSWWWW",
+    "HTHSTHSSSTWWWWWWW",
+    "THSHSTHSSSWWWWWWW",
+    "HTHSSTHSWWWWWWW",
+    "HTHSTHSSSTWWWWW",
+    "THSTHTHTWW",
+    "HSTHSSTHSTWW",
+    "THSHSTHSSTW",
+    "HSHTHSSSW",
+    "HTHSTWWWWW",
+    "HTHSSSTHSTWWWWWWW",
+    "HSHSTHS",
+    "SSSHWW",
+    "STHTHSSTHSTWWWWWWW",
+    "THSTHSSSTHSSS",
+    "THSHSSTHSSWWWWWW",
+    "HTHSTHSSTWWWWWWW",
+    "THTHTWWWWWW",
+    "HTHSSTHSSSW",
+    "SHTHSTHWWWWWWW",
+    "HTHSTHSSTWWWWWW",
+    "HTHSTHSSTWWWW",
+    "HSTHSSTHTWWWWWWW",
+    "SHSTHTHSTWWWWWWW",
+    "HTHSTHSSTWWW",
+    "HTHSSSHWWWWWW",
+    "HTWWW",
+    "THSHTHTWW",
+    "THSTHSTHSSSTWWW",
+    "HTHSTHSSWWWWWWW",
+    "THSTHSSSTHSTW",
+    "SSSHSSWWWWWWW",
+    "HTHSTHSS",
+    "HSHTHSWWWWWWW",
+    "SHSTHSSSTHSS",
+    "HTHSTHSTWWWWWW",
+    "HTHSTHSTWW",
+    "THSTHSSSTHSSSWWW",
+    "HSHSSSTHS",
+    "HTHSTHSTW",
+    "STHTHSTHSTWWWWW",
+    "THSHSTHW",
+    "HTHSTHSWWWWWWW",
+    "HTHSTHSWWWWW",
+    "HTHTWWWWWWW",
+    "THTHSTHSSTWWWW",
+    "SHTHSSSTHSWWWWWW",
+    "STHSWWWW",
+    "STHSTHTHT",
+    "HTHSSSTHSSTWWWWWWW",
+    "HTHSTHSSTW",
+    "SSHSSSWWWWW",
+    "HSHSSSHSSWWW",
+    "STHSTHTHSSSW",
+    "THSHSSSTHSSS",
+    "SHTHSSSTHWWWW",
+    "HTHSTHTWWWWWWW",
+    "HTHSHTW",
+    "SHSSSW",
+    "SSSWW",
+    "HTHSTHTW",
+    "HTHSHWW",
+    "HTHSTHWWWW",
+    "HTHSSSHTWWWWW",
+    "HSHSTHSSSTWWWWW",
+    "HSHTHSSTWWW",
+    "SSTHSW",
+    "THTHSSSHSSSTWWWWWW",
+    "SHSTHTHSSST",
+    "HTHSTWWWWWW",
+    "HTHSTWWWW",
+    "THTHTHWWWW",
+    "HTHSTWWW",
+    "STHTHTHSSSTWWW",
+    "HTHSTWW",
+    "HTHST",
+    "HTHSHSSSTWWWWWWW",
+    "SHTHTH",
+    "SSTHSTWW",
+    "THTHSSSTHSSW",
+    "SHSTHTHWW",
+    "THTHSTHSSSTWWWWW",
+    "HSTHSSTHSSSWW",
+    "HTHSHSSSWWWWW",
+    "HTHSHSSSWWW",
+    "HSHSSSHSW",
+    "THTHSTHSWWWW",
+    "THSHTHSSSTWWWWWW",
+    "HSTHSSSTHSSWWWWWW",
+    "THSHSSTHSSWWWWWWW",
+    "HTHSHSSSWW",
+    "HTHSHSSS",
+    "THTHSSTHSWWWWWWW",
+    "HTHSSSTHWWWWWWW",
+    "HTHSHSSTWWWWWWW",
+    "HTHSTHSTWWW",
+    "STHTHSTHSTW",
+    "HTHSHSSTWWWW",
+    "STHSTHTHSSSTWWWWWW",
+    "SSSHSTWWWW",
+    "SHSTHSTHSW",
+    "THSWWWW",
+    "HTHSHSSSTWWWWW",
+    "HSTHSTHSSTWWWWWW",
+    "THSTHSSSTHSSTWWWWW",
+    "HTHSHSSWWWWWWW",
+    "STHST",
+    "HTHSSSHST",
+    "SHSTHTHSSSWWWWWWW",
+    "IWWW",
+    "THTW",
+    "HTHSSSHSTW",
+    "HTHSTHSSW",
+    "HTHSHSS",
+    "HTHSSSTWWWWWWW",
+    "THSHSSTHSTWWW",
+    "HTHSSSTWWWWWW",
+    "THTHSSSTHSSSWWWWWWW",
+    "HTHSHSTWWWW",
+    "HSTHSSSHSSW",
+    "STHSTHSTHT",
+    "HTHSHSWWWWWWW",
+    "HTHSHSWWWWWW",
+    "SSSHSWWWWWW",
+    "THTHTHSWWW",
+    "STHSTHTHSSSTWWWW",
+    "HTHSHSWWW",
+    "HTHSTHSSSTWW",
+    "HTHSHSWW",
+    "SHTHSTHSSSWW",
+    "HTHSTHSSSWWW",
+    "SHTHSTHTWWW",
+    "HTHSHSW",
+    "HTHTHSTWWWWWWW",
+    "HTHWWWWW",
+    "HTHSHTWWWWWWW",
+    "STHTHTHSSTWWWWW",
+    "STHSSSTWWWW",
+    "SSHTWWWW",
+    "STHTHTHSSSTWWWWWWW",
+    "HTHTHSSW",
+    "HSHSTHSSS",
+    "HTHSHTWWWWWW",
+    "STHSTHSTHSSST",
+    "HSTHTHSSWWWWWW",
+    "HTHSSTW",
+    "HTHSHTWWWWW",
+    "HTHSSTHSSTWW",
+    "SSTHSSWWWWWWW",
+    "HTHSHTWWWW",
+    "HTHSHSSWWWWW",
+    "HTHSHSSTW",
+    "HSTHSSSTHSSWWWWW",
+    "HSHTHTWWWWWWW",
+    "HTHSHWWWWWWW",
+    "STHSTHSSSTHTWWWW",
+    "HTHSSSHSSSTWW",
+    "STHTHSTHSSTWWWWWWW",
+    "HTHSHWWWWWW",
+    "HTHSSTHSTW",
+    "HTHSHWWWWW",
+    "HTHSHWWWW",
+    "HSTHSSTHSSSTWWWWWW",
+    "STHTHSTHTWWWWWWW",
+    "HTHSSSHTWWW",
+    "STHSTHSTHS",
+    "SSWWWWWWW",
+    "HTHSHW",
+    "STHSTHSSSTHSSSW",
+    "HTHSH",
+    "HTHSWWWWWWW",
+    "HTHSTHSSWWWWWW",
+    "HSHSSSTHSTWWW",
+    "STHSTHTHSSSTWWWWW",
+    "THTHSHSSWWWWWWW",
+    "THTHSSTHSSWWWWWWW",
+    "STHTHSSTHWWWWWW",
+    "HSHSSSTHTWWW",
+    "HTHS",
+    "HTHSSTHWWWWWWW",
+    "SHSTHSSSTHTWWWWWW",
+    "HTHSSTHTWWWWWWW",
+    "THTHSSTHWWWWW",
+    "STHSTHSSTHSSWW",
+    "HTHTHSSSTWWWWWWW",
+    "HSHTHSSSTWWWWWWW",
+    "THSHTHSSWWWWWW",
+    "HTHSW",
+    "THSTHSSSHWWWW",
+    "HTHSSSTHWWWWWW",
+    "SHSTHSTHSSSTWWWWWWW",
+    "HTHTHSSSTWWWWW",
+    "THSTHSSSTHWWW",
+    "THTHSSSHSST",
+    "THSTHTHSSSWWW",
+    "HTHSSSTHSWWWWWW",
+    "HSHTHWWW",
+    "HSTHSSSHSTWW",
+    "HTHTHSSSTWW",
+    "STHSTHSSTHSSSTWWWWWW",
+    "THSTHSSTHSWWWW",
+    "HTHSSTHSTWW",
+    "HTHTHSSSTW",
+    "THSHSTHSWWWWW",
+    "HTHSSSHSSTWWWW",
+    "HTHTHSSSWWWW",
+    "HTHSSWWW",
+    "HTHSSS",
+    "HTHTHSTWWWWWW",
+    "HTHTHSSSWWW",
+    "STHSTHSTHSWWWWWWW",
+    "HSHTHWWWWWWW",
+    "HSTHSSSHSSSTWW",
+    "THSHSSTHSSSTWWWW",
+    "HTHSSTHSTWWWWWW",
+    "SSHTWWWWWWW",
+    "HTHTHSSSWW",
+    "THSTHSSSTHSWW",
+    "HSTHSTHSSTWWWWW",
+    "HSHTHSSTWWWWWW",
+    "HTHSSSH",
+    "HTHTHSSTWWWWWWW",
+    "HTHTHSSTWWWWWW",
+    "STHSTHSTHSTWWWWWW",
+    "HTHSSSTHSSWWWWWW",
+    "SSSTHSST",
+    "STHTHTHSST",
+    "HSHSSTHSWWW",
+    "HTHSTHSWW",
+    "HTHTWWWWW",
+    "HTHTHSSTW",
+    "HSHSSSTHSSSWWW",
+    "THSTHSTHW",
+    "HTHSTHWWWWWW",
+    "HTHTHSST",
+    "SHSTHSSTHSSWWWWWW",
+    "HSHSSSHST",
+    "STHSTHSTHTWWWWW",
+    "HTHTHSSWWWWWWW",
+    "SHSTHSSSTHSSSTWWWWW",
+    "HTHSSSHSSSW",
+    "HTHTHSSWWWWW",
+    "THTHSSSTHSSSTWWWWW",
+    "HTHSSWW",
+    "HSHTHSSTWWWWW",
+    "STHTHSSSTHSSSWWWWWW",
+    "HTHTHSSWWWW",
+    "HTHTHSS",
+    "THSTHSSTHSSSWWW",
+    "HTHSSSHSWW",
+    "SHSTHSSTHSSSTW",
+    "STHTW",
+    "SHSTHTHSSTWWWWWW",
+    "HTHTHSTWW",
+    "THTH",
+    "HTHTHSTW",
+    "HSHSSSHSSSWW",
+    "HTHTHSWWWWWWW",
+    "HSHSSTHSST",
+    "HSHSSSTHSSSTWWW",
+    "HSHSSSTHSSSTWWWW",
+    "STHTHTHWWWW",
+    "HTHSHST",
+    "HSTHSTHTWWWWWWW",
+    "STHSTHTHSSWWWWWWW",
+    "HTHTHSWWWWWW",
+    "THTHSSSWWWWWW",
+    "HTHSSSHSTWWWWW",
+    "STHTHSSTHTWWWWWWW",
+    "HTHTHSWW",
+    "THTHSTHSSSWWW",
+    "HTHSHTWWW",
+    "HTHSSTHTWWWW",
+    "SHTHSTHSSTWWW",
+    "THTHSSSHSSSWWWW",
+    "HSTHTHSSWWWWW",
+    "HTHTHTWWWWW",
+    "HTHTHTWWWW",
+    "TWWW",
+    "HTHSSSTHSSSTWWWWW",
+    "SHSTHSSTHSSSTWW",
+    "IWWWW",
+    "STHTHSTHSSTW",
+    "HTHTHWWWWWWW",
+    "HTHTH",
+    "HTHTWWWWWW",
+    "THSTHSSSHSSWWWW",
+    "HTHSSSHSTWWW",
+    "HSTHSSTHST",
+    "STHSTHSSTHSSTWWWWWW",
+    "THSHSSSTHWW",
+    "HTHTWW",
+    "HTHSSTHSSSWWWWW",
+    "HTHTW",
+    "STHTHSSTHSSSTWWW",
+    "HTHSHSTWWWWWWW",
+    "HSHSSTHSW",
+    "STHSTHSSSTHSSTWWWW",
+    "SHSTHSSSTHSTWWWWWW",
+    "HTHSSTHTWWWWW",
+    "THSTWWWWWW",
+    "SHSSSWW",
+    "SSHSTWWWW",
+    "THTHTHSSSWWWWW",
+    "HTHWWWW",
+    "HTHWWW",
+    "SSSHSSTWWWW",
+    "HSHSSSHSSWWWWWW",
+    "HTHWW",
+    "THTHSSSHSSSTWWWWWWW",
+    "SHSSTWWW",
+    "THTHSSSHW",
+    "SSSTHSSSTWWWWWWW",
+    "SSSTHSSSTWWWWW",
+    "SSSWWWW",
+    "THSTHTHSW",
+    "SSSHWWWWWWW",
+    "THTHSSSTHSTWWW",
+    "THTHSTHSTWWWWWWW",
+    "STHTHSTHSS",
+    "THTHSSSHST",
+    "HTHSHSSTWWW",
+    "STHSTHTHW",
+    "SSSTHSSSTWWW",
+    "SSSTHSSST",
+    "THSTHSSSTHSSSWWWWWWW",
+    "THWWWWWWW",
+    "HTHSHSWWWW",
+    "STHSTW",
+    "THTHTHSSSTWWW",
+    "STHSTHSSSTHSWWWW",
+    "HSTHSTHSSWWW",
+    "THSTHSTHSSWWWWWW",
+    "SSSTHSSSWWWWWW",
+    "SHSTHSSTHSTWWWWWW",
+    "THTHTHSSSTW",
+    "SSSTHSSSWWWWW",
+    "HSTHSSSHSWWWWW",
+    "SHTHSTHSSWW",
+    "THTHSSTHSSS",
+    "SSSTHSSSWWWW",
+    "HSSST",
+    "THTHTHSTWWWWWWW",
+    "SSSTHSSSWWW",
+    "THTHSSTH",
+    "SSSTHSSSWW",
+    "SSSTHSSTWWWWWW",
+    "STHSSSTW",
+    "SHTHSSTHTWWWWWWW",
+    "SSSTHSSTWWWWW",
+    "THTHSSSTHTWWW",
+    "SSSTHSSTWWWW",
+    "HSTHSSSTHSSSTWWWW",
+    "THSHTHSTWWWWWW",
+    "STHSSSW",
+    "THS",
+    "STHSSSTWWWWWWW",
+    "THSTHSSSHSSSTWWWWW",
+    "SSSTHSSWWW",
+    "STHSTHSTHWWWWWWW",
+    "SSSTHSSWW",
+    "HSTHSSSTHW",
+    "HTHSTHST",
+    "SSSTHSSW",
+    "HTHSTHSSSWWWWW",
+    "HSHTHSTWWWWW",
+    "SSSTHSTWWWWWW",
+    "HTH",
+    "THTHTHSSTWWWWWWW",
+    "HTHSSTHSSS",
+    "HSHSTHSSSWWWWW",
+    "STHSTWW",
+    "STHSWW",
+    "SSHS",
+    "HSTHSSSTHSSWW",
+    "STHTWWWWWWW",
+    "HTHTHSSSTWWWW",
+    "HTHSWWW",
+    "THSTWW",
+    "STHSTHSSTHSST",
+    "STHTHSTHSTWWWWWW",
+    "SHSTHSTHSSSTWWW",
+    "HTHSTHSSSW",
+    "HTHTHTW",
+    "HWWWWWWW",
+    "HSS",
+    "SHTHSTHSSSWWWWWWW",
+    "HSHSSSHSSSWWWW",
+    "THSTHSSTHWWWWWW",
+    "HTHTHTWW",
+    "SHTHSSTHSSSTWW",
+    "THTHSTHSSSTW",
+    "HSWWW",
+    "THTHWWWWW",
+    "STHWW",
+    "SHSSSTWWWWW",
+    "HSHSTHWWWWW",
+    "HSTHTHWWWWWW",
+    "HSTHSSSTHSSTWWWWWWW",
+    "THTHSSSTHSSSWWWWWW",
+    "HTHW",
+    "SSHST",
+    "SHTHSSSTHSSSWWWWWWW",
+    "STHSTWWW",
+    "HSHSTHSSSTWWW",
+    "HTHSTHSSWW",
+    "THTHT",
+    "SHSSSTWWWW",
+    "THSTHSSSHTWWWWW",
+    "HTHSSSTHSSSWWWWWW",
+    "HSTHTHSS",
+    "STHTHTHST",
+    "HTHSHSSSTW",
+    "THSTHSTHS",
+    "SSSTHSSWWWWW",
+    "HTHTHSTWWW",
+    "STHTHSSSTHSSST",
+    "THSHTHSSSTWWWW",
+    "THSHSTHSSSTWWWWWW",
+    "SSSHSSTWW",
+    "SSTWWWWWWW",
+    "THTHSTHTW",
+    "HTHSSSTHSSSWWWW",
+    "SHSSSWWWWWWW",
+    "STHSTHTHTWWWWWW",
+    "HSHSTHTWWWW",
+    "STHSTWWWWWWW",
+    "SHSSS",
+    "THSSSTW",
+    "HTHSSSTHSSTWWW",
+    "SHSSW",
+    "SHSSTWWWW",
+    "SHTHSSTHSSSTWWWWW",
+    "HSSSTWW",
+    "HTWWWW",
+    "THSHSTHTWW",
+    "SHTHSSSTHSTWW",
+    "SHSSTWWWWWWW",
+    "HTHSSTHWWW",
+    "THTHSTHWWWW",
+    "STHSSSTWWWWWW",
+    "STHSTHSSTHWWWWWW",
+    "STWWW",
+    "SHSSSWWWWW",
+    "STHTHTHSSWWW",
+    "SHSSWWWWWWW",
+    "SHSSWWWWWW",
+    "HSHSSTH",
+    "THSHSTHSSSTWWWWWWW",
+    "SHSSWW",
+    "STHSTHTHWWWW",
+    "HTHTHWWWW",
+    "THTHSSTHSWWWW",
+    "THSHSSTHSSSW",
+    "SHSST",
+    "HTHSSSTHSST",
+    "HTHSSSHTWWWW",
+    "HSTHSTHSWWWWW",
+    "THTHSHSSSWWWWWW",
+    "HTHSSSW",
+    "HTHSSSHSSSTWWWWWWW",
+    "THTHSSTHSSSTW",
+    "HTHWWWWWWW",
+    "HTHSSSHSSSWWWW",
+    "SHSSSTWWW",
+    "HSHSSTHSSTWWWWW",
+    "HTHSTHSSS",
+    "THSSW",
+    "HTHSSTHSTWWW",
+    "SSHWWW",
+    "STHTHSSSTHSWWW",
+    "THTHSSTHSTWWWWWW",
+    "SSHTW",
+    "SHSWW",
+    "HSTHSSSTHSSTWWW",
+    "SSW",
+    "HSSSWWW",
+    "SHSSST",
+    "HSTHSSSTHSSWWWW",
+    "SHTWWWWWWW",
+    "THSTHSSTHSTWWWW",
+    "HSHSSTHSSSWWW",
+    "THSHSTHTWWWWW",
+    "SSHSTWWWWW",
+    "THTHSSSTWWW",
+    "HTHSSTHSSSWWW",
+    "HTHTHW",
+    "THTHSSTHWWW",
+    "SHTWWWWWW",
+    "HTHSTWWWWWWW",
+    "HSHSSTHSTWWWWW",
+    "HWWWWW",
+    "SSSHSSST",
+    "SHTWWWWW",
+    "SHTWW",
+    "SHTW",
+    "STHSTHTHSSSTW",
+    "SSSTHSSSTWWWWWW",
+    "SHSTHSSSTHSSSTWWWW",
+    "HSHSSSHSTW",
+    "SHWWWWWWW",
+    "SSHSSTWWW",
+    "HSTHSSSHSWWWWWWW",
+    "SHTWWW",
+    "THTHSSSTHSWWW",
+    "HST",
+    "SSHSS",
+    "THTHSSTHSSSWWWWWWW",
+    "SSTHSSSTWWW",
+    "HTHSSSHTWWWWWW",
+    "SHWWWWW",
+    "SWWW",
+    "HTHTHSW",
+    "SHSSSTWWWWWW",
+    "HSHSTHW",
+    "HSHSTHSSST",
+    "STHSTHSTHSSSTW",
+    "THTHTHSSWWWWWWW",
+    "THSHSSSTHSSSW",
+    "STHTWWWWWW",
+    "SHTHSTHSSSTWWWWWW",
+    "HTHSSSWWW",
+    "SSHSSSWWW",
+    "SSTHTW",
+    "SSSHSSTWWW",
+    "SHWWWWWW",
+    "SWW",
+    "HSHSSSHSST",
+    "SHSSTWWWWWW",
+    "SHSTHSSSTHSSWWWWWWW",
+    "HSTHTHSSSTWWWW",
+    "THSTW",
+    "SW",
+    "SHST",
+    "S",
+    "HSHTHSSWWW",
+    "HTHSHSTWW",
+    "THSSSTWWWWWWW",
+    "HTHTHTWWW",
+    "STHTWWWWW",
+    "HTHTHSWWWWW",
+    "HTHTHSSST",
+    "THSSTWW",
+    "THSSSWWWWWWW",
+    "HTHSTHSWWWW",
+    "THSSSWWWWWW",
+    "SSTWW",
+    "THSSSWWWW",
+    "STHSS",
+    "SHSTHSSSTH",
+    "HSHTHTWWW",
+    "THSTHSSSTHSSWWWWW",
+    "SSTHSSWWWW",
+    "THSSSWWW",
+    "THSSS",
+    "SSSHSWW",
+    "HSSTWWWWWW",
+    "THTHSSTHTWWWWWWW",
+    "SSSTWWWWW",
+    "SSTHSSST",
+    "STHTHSTHSSWWWWWWW",
+    "SHTHTHSSW",
+    "HSSTW",
+    "HTHSHSSST",
+    "STHTHSSSTHSTWW",
+    "SHSSWWWW",
+    "THTHSSSTHSSTWWWWWWW",
+    "SSSHSSSWW",
+    "THSHSTHSSSWWWW",
+    "THSTHSSSTH",
+    "HSSWW",
+    "THSHSSTHSS",
+    "SSHTWW",
+    "HTHSSSTHSSSTWWWWWWW",
+    "HSTHTHSSSWWW",
+    "THTHSSSTHTW",
+    "THSHTHSSSWWWWW",
+    "HTHSSTHSTWWWWW",
+    "TWWWWWW",
+    "STHTHSSSTHSSWWWWW",
+    "SSSHST",
+    "HSSTWWWW",
+    "SHSTWWWW",
+    "HSHSSSTHST",
+    "HSTHSSSHTWWWWWWW",
+    "HTHSSSHSSTW",
+    "HSWWWWWWW",
+    "THTHSSSHSSTWWW",
+    "HSTHSSSTHSSS",
+    "SSSHSSTW",
+    "HSTHSSSHSSSWWWWWWW",
+    "HTHTHSSSTWWW",
+    "THST",
+    "SSSHSWWWW",
+    "THTHSSSHSSTW",
+    "SSTHSST",
+    "THTHSSSTHSTWW",
+    "THSWWWWWW",
+    "HSHSTHSSTWWW",
+    "HSSTWW",
+    "HSTHSSSHSSWWWWWW",
+    "SSTHWWW",
+    "THSTHSSTHWWWW",
+    "HSTHSSSTHSSSWWW",
+    "STHSTHSSSTHTW",
+    "SHSSTW",
+    "SHSTWWWWW",
+    "THTHSSSTHSSSWWWW",
+    "THWWW",
+    "STHWWWW",
+    "HTHSSSTHSTWWW",
+    "SSSTWWWW",
+    "HTHTHSSTWWWW",
+    "SHTHSSTHTWWWWWW",
+    "THTHTHSSTWWW",
+    "SSTHSWWWWWWW",
+    "HTHTHSSSWWWWWWW",
+    "STHSWWW",
+    "HTHTHSSSW",
+    "SSSHSST",
+    "STHTHSSTHS",
+    "THTHSSSTHTWW",
+    "HTHSTW",
+    "SHTHSSSTHSSSTWWWW",
+    "SSSHTWWWWW",
+    "HTHSTHSTWWWWWWW",
+    "HTHSTHWWWWWWW",
+    "STHWWWWWWW",
+    "SHTHSTHSSTWW",
+    "SSHT",
+    "HTHSSTHSSSWW",
+    "HTHTHSSWW",
+    "HSHTHSSSWWWWWW",
+    "HTHSWWWWWW",
+    "HTHSSTHSWWW",
+    "HSTHSTHSTWWWW",
+    "STHTHSTHSSSWWW",
+    "SHSTHSSSTHSSW",
+    "HTHSTHSTWWWWW",
+    "STHSSWWWWWW",
+    "STHSTHSSTHTWW",
+    "HTHSSSTHSSWWW",
+    "HTHTHSSTWW",
+    "HSHSSSTHWWWWW",
+    "HTHSTHW",
+    "THSHSTHSW",
+    "HSSW",
+    "THTHSSSHTWWW",
+    "STHSTHSSSTHSSS",
+    "HSSSTWWWWWWW",
+    "THSHSSTHSSS",
+    "HSHTHSSSWWWWWWW",
+    "HSTHTHSSSTWWWWWWW",
+    "HTHSSSTHSTWWWWWW",
+    "STHSTHSTHSTWW",
+    "STWWWWW",
+    "THW",
+    "HTHSTHSWWWWWW",
+    "HTHSSTHW",
+    "HSWWWWW",
+    "STHSWWWWWW",
+    "STHTWWWW",
+    "HTHSSTHSWWWWWW",
+    "STHSSSWWW",
+    "HTHTHTWWWWWWW",
+    "HSHSTHSSSWWWWWWW",
+    "SHTHSSTHSTWWWWWWW",
+    "HTHSSSTHSTWWWW",
+    "HT",
+    "STHSTHSSSTHWWWW",
+    "HTHSSSHSSWW",
+    "SSSTHSSTWW",
+    "THSSWWWWW",
+    "SHTHTHSSWWWWWW",
+    "THSTHSSSTHSSWWW",
+    "THTHSSTHSSSWWWWW",
+    "HWWWW",
+    "STHSTHTHTWWWWW",
+    "SHSSSTWWWWWWW",
+    "HSTWWWWWWW",
+    "HSST",
+    "HSTHSSTHWWWW",
+    "STHTHSSSTHSTW",
+    "IWWWWWWW",
+    "SSHSSSWWWW",
+    "HSHSSSTHSW",
+    "IWWWWWW",
+    "SHSTHTHWWW",
+    "THSTHSSSTHSTWWWW",
+    "STHSSTWWW",
+    "HTW",
+    "SSSHSTWWWWWWW",
+    "HTHSSTHSS",
+    "STHSTHSTHSSWWWW",
+    "SSSHSWWWWWWW",
+    "THSTHSSSTHSSSWWWW",
+    "SSTHSWW",
+    "SSSTHSSTW",
+    "SSTHSSSTWWWWWWW",
+    "STHSTHSTHSSSWWW",
+    "STHTHSSTHSSTWWWWWWW",
+    "HSTHSTHSWWWW",
+    "HSTHSSTHSSW",
+    "STHTHSSTHSSSTW",
+    "THSHSSSTHSSSWWW",
+    "STHW",
+    "SSHSTWW",
+    "SHSTW",
+    "STHTHTHSWWWWWW",
+    "SHSTHTHW",
+    "THSST",
+    "THSWWWWWWW",
+    "HSTHTHSSSTWWWWWW",
+    "SHSTHSSSTHSW",
+    "HSTHTHW",
+    "HTHTHSSTWWW",
+    "HSTHSSTHSSTWWWWWWW",
+    "STHSTHTHSTWWW",
+    "THSTHTHSSTWWWWWWW",
+    "HTHSTHSSTWW",
+    "SSTHSSS",
+    "HSHSTHSSW",
+    "STHTHTHSSTWW",
+    "THSHSTHTWWWWWWW",
+    "SHSSSTWW",
+    "SSHSSST",
+    "HTHSSSTHSSWWWW",
+    "HTHSSSTHTW",
+    "I",
+    "SSHSSTWWWWWWW",
+    "SHSTHSSTHSSSTWWWWWW",
+    "THTHSSTHSTWWWW",
+    "HWWW",
+    "THTHSSWWWW",
+    "STHSWWWWW",
+    "STHSTHTHSSWWWW",
+    "THTHSSSHSTWW",
+    "HSHSTHTWWWWW",
+    "HSHSTHTW",
+    "HTHWWWWWW",
+    "HSHSSSTHWWWW",
+    "SSHSSWWWWWW",
+    "SSSHT",
+    "SSSHSSSWWWWWWW",
+    "SSTHSSSW",
+    "HSTHTHTWWWWW",
+    "HSTHSSSHSSTWW",
+    "THTHTHSSSWWWWWW",
+    "THSSSWWWWW",
+    "HSHSSTHTWWW",
+    "THTHSSTHSSSWWWW",
+    "SHSTHTHSTWWWWW",
+    "HTHSHSTWWWWWW",
+    "SSTWWWWWW",
+    "HSHTHSTWWWWWWW",
+    "HSTHTHSSSWWWWWW",
+    "SHSTHSSTHSTW",
+    "SHSTHTHTW",
+    "THSTHSSSTHTWWWWWWW",
+    "SSTWWWWW",
+    "SHSWWWW",
+    "HTHTWWWW",
+    "SHSTHSSSTHSSWWWW",
+    "SSSTHSSWWWWWWW",
+    "THSHSTHTWWWW",
+    "HSHSSTHTWWWWWW",
+    "SSSTHT",
+    "SHSTHSSTHSSWWWWWWW",
+    "HSSWWWWW",
+    "SSSHWWWWWW",
+    "THSHSSTHSSST",
+    "HTHSTHSSSTW",
+    "SHSTHSTHWWW",
+    "STHSW",
+    "HTHSHSSSW",
+    "SHSTWWW",
+    "THTHSSTHSSWW",
+    "THSSWWWWWW",
+    "THTHTHSSS",
+    "HSTWWWWWW",
+    "HTHSSSTHSW",
+    "THTHSSWWWWW",
+    "HTWW",
+    "THTHSHSSTWW",
+    "HTHSHTWW",
+    "HSHSSSHWWWWWWW",
+    "HSTHSSTHSSWWW",
+    "THTHSHSS",
+    "SHSWWWWWWW",
+    "THSTHSSTHSSWWWWW",
+    "THTHSSTWWWWWWW",
+    "SHSWWW",
+    "HSHSTHSSSWWWW",
+    "HTHSSSTHSSSTW",
+    "SSSTHWWWWW",
+    "STHSTHSTHSTW",
+    "SSTHSTWWW",
+    "THSSTWWWWWWW",
+    "THTHSSSTHSSTWW",
+    "THSSTWWWW",
+    "STW",
+    "HSTHSSTHS",
+    "STHTHSSTHSSWWW",
+    "SSHSSSTWW",
+    "SHTHSTH",
+    "HTHSSTH",
+    "THTHSSSTHSWW",
+    "HTHSSSHSTWWWWWW",
+    "HTHSSSTHTWWWW",
+    "STHSTHTHSWWWW",
+    "HTWWWWWW",
+    "STHTHSSSTHSSSWWWW",
+    "HTHSHSSWWW",
+    "STHSTHSTHSSTW",
+    "HSTHSSSTHSSTWWWWW",
+    "SSWWWW",
+    "HTHSSSHSW",
+    "TWWWWWWW",
+    "STHWWWWWW",
+    "SSHWWWWW",
+    "STHSTHTHSSSWWWWWWW",
+    "HSTHSSSTHSSSWWWWW",
+    "IW",
+    "SHTHSSSTHS",
+    "SSWWW",
+    "HSWW",
+    "HSTWWWWW",
+    "HSSSWWWWWW",
+    "THSTHSSSHSSWWWWWWW",
+    "HSSTWWW",
+    "HS",
+    "SHSTHTHSSTWWWWW",
+    "HSSSTWWWWW",
+    "HTHSSSTHSSSW",
+    "SSHSWWWW",
+    "SSHTWWWWWW",
+    "SHSTHSTHSSSTW",
+    "THTWWWWWW",
+    "HTHSSSTHTWWWWWWW",
+    "THTHTHSSSTWWWW",
+    "SHTHSTHTWWWWWW",
+    "SSHSSSTWWWWWW",
+    "SSTHSSTWWWWWW",
+    "HSHTHSWWWWWW",
+    "STH",
+    "THTHTWWW",
+    "HSSSTWWW",
+    "SHSSWWW",
+    "SHS",
+    "HTWWWWW",
+    "STHSTHTHSSTWWWWWW",
+    "THTHSHSWW",
+    "THSTWWWW",
+    "STHSTHTHSTWWWWWWW",
+    "SHTHSSTHSSSTWWWWWW",
+    "STHSSWWWWWWW",
+    "HSSTWWWWWWW",
+    "SHSSWWWWW",
+    "HTHSSSHSSWWWW",
+    "SHTHSSSTHSSWWWW",
+    "THTHSSSTWWWWW",
+    "THWWWW",
+    "HSSSTWWWWWW",
+    "STHWWWWW",
+    "STHTHTHSSS",
+    "SSHSSS",
+    "HSTWWWW",
+    "THTHSTHSTWWWWW",
+    "HTHSHT",
+    "HSTWW",
+    "SHTHTHSWWWWW",
+    "STHSSSWWWWWW",
+    "HSTHTHWWWWW",
+    "TH",
+    "HTHSTHSSWWW",
+    "THTHSHSSWW",
+    "THWWWWWW",
+    "SHSTHSTHSSWWWWWW",
+    "SHSTHTHSSTW",
+    "THSHSSSTHSSWWWW",
+    "SHTHTHTWWWWWW",
+    "SSSHSTWWW",
+    "HSTHSSSHSW",
+    "STHSTHSTHST",
+    "THSWW",
+    "THTWW",
+    "HSHSSSHTWW",
+    "THSTHSSTHSSSWW",
+    "HSHSSSHSSWW",
+    "HSHTHSWW",
+    "THTHSHSSSW",
+    "HTHSTHSSSTWWWWWW",
+    "SSTHSSSWWWWW",
+    "HTHSSSTHST",
+    "HTHSSSTHWWWW",
+    "THTWWW",
+    "SHSSSWWW",
+    "HTHSTHTWWWWW",
+    "HTHSTHWWW",
+    "THTHSSTHSSSWWWWWW",
+    "THSTHSSSHSST",
+    "TWWWWW",
+    "STHTHSSSTHTWWWW",
+    "THSTHSSTHSWWW",
+    "THSHSSSTHSSTWWWW",
+    "HTHSTHSSSWWWWWWW",
+    "SSTHSWWW",
+    "HSTHSTHWWWWW",
+    "SSSTHSSSTWW",
+    "THSW",
+    "SHSS",
+    "THSHTHSST",
+    "HTHTHSSSWWWWWW",
+    "SHTHTHSSTWWWWWWW",
+    "THSS",
+    "SHT",
+    "HTHSSTHTWWWWWW",
+    "HTHSSTHSSSWWWWWWW",
+    "THSSSTWWWWWW",
+    "THSTHSSTHTWWWWW",
+    "HTHSTHTWWW",
+    "SSS",
+    "STHTHSSTHSSSTWW",
+    "SSTHS",
+    "HTHSSSTHSSSTWWWWWW",
+    "HSTHTHTWWWWWW",
+    "STHTHSTHSSTWWWWWW",
+    "THSTHSSTHSSSTW",
+    "SSSTHSTWWWWWWW",
+    "SSTHTWWWW",
+    "HSTHSSSTHSS",
+    "SHTHSTHSWWWWWWW",
+    "HTHSSSHSSSTWWWWWW",
+    "STHTHSSTHSSTWWWWW",
+    "HTHSSSTHSS",
+    "STHTHSSTHSTWWWW",
+    "SSSHSSSTWWWW",
+    "THSTWWWWWWW",
+    "SSST",
+    "SSHSSWWWW",
+    "THTWWWWW",
+    "THSHSSTHTWWWWW",
+    "SHSSSWWWWWW",
+    "THSSWWWW",
+    "THSSWWW",
+    "HTHTHSSS",
+    "HSHSSTHSSTW",
+    "THSSTW",
+    "THSHSSSTHS",
+    "HSTHSTHWW",
+    "SHSTWW",
+    "THTHSTHSSTWWWWW",
+    "STHSTHSSTHSSSTWWW",
+    "THSSTWWW",
+    "THSSSTWWWW",
+    "STHTHSSTHWWWWW",
+    "HTHTHSSSWWWWW",
+    "SHTHSTHSSSTW",
+    "THTHTHTWWWWWWW",
+    "THSHSSTHWWW",
+    "HSSSW",
+    "THTHSTH",
+    "HSSSTWWWW",
+    "HTHSHSST",
+    "HTHSSTHSSSTWWWW",
+    "SSTHSSSWWWWWWW",
+    "STHTHSSSTHSSW",
+    "HSHSSTHSTWWWWWW",
+    "STHTHSSSTHSWW",
+    "THSTHSSTHSSTWWWWW",
+    "STHSSWWW",
+    "THSTHTHSS",
+    "HSTHSSSTHSSSTWW",
+    "HTHSSSTHTWWWWWW",
+    "HSHSTHSSWWWWWWW",
+    "THSHTHSSSTWWWWWWW",
+    "HTHSTHS",
+    "HSHSSTHWWW",
+    "HSTHSSSTHSSST",
+    "HSHTHSWWWW",
+    "HSTHTHTWWWW",
+    "THTHSSSTHSSWWWWW",
+    "THSTHSSSTHSSWWWWWW",
+    "HTHSSTWWWWWW",
+    "THT",
+    "SSSTHW",
+    "HTHSTHSSSWWWWWW",
+    "STHSSTW",
+    "HSTHTHSSTWWWWWW",
+    "THTHTHSWWWWWWW",
+    "SSHSSWWWWW",
+    "STHSTHSSTHSSSWWWWW",
+    "STHSSTWW",
+    "HSTHSSSHSTW",
+    "SSTHSSWW",
+    "SSSTHTWWWWWWW",
+    "SSSHSSSWWWW",
+    "THTHSHWWWWWWW",
+    "HSSWWWWWWW",
+    "HTHSTHTWWWW",
+    "THTHSHSSWWW",
+    "THTHWWWWWWW",
+    "HSHSSSTHTWW",
+    "STHSSTWWWWW",
+    "SHTHSTHSTWWWWWW",
+    "STWWWWWWW",
+    "HSTWWW",
+    "STHSSSWWWW",
+    "THTHSHSTW",
+    "STHSSSWWWWW",
+    "STHSSSWWWWWWW",
+    "STHSSSTWWW",
+    "SSSHTWW",
+    "SSTHSSSTWW",
+    "THSTHTHSWWWWWW",
+    "HSTHSSSHSSWWWWW",
+    "THTHSHSTWWW",
+    "HTHSSTHSSSTWWWWW",
+    "THTHSHSSTWWW",
+    "THSTHSTHSTWWWW",
+    "THSHSSSTHSSSWWWWWWW",
+    "THSWWWWW",
+    "THSTHSSSTHWWWWW",
+    "THSTHTHSSWWWW",
+    "SSHSSWWW",
+    "HSHSTHSTWWWWWW",
+    "THSHTHSW",
+    "HTHSTHWW",
+    "HTHSHSSSWWWWWWW",
+    "THTHTWWWWW",
+    "HTHSHSTWWWWW",
+    "SSSHTW",
+    "THTHSSTHSSSTWWWW",
+    "HTHSHWWW",
+    "HSTHSTHSSSTWWWWWW",
+    "HSTHSSSTHS",
+    "SSWW",
+    "SSTHWWWWWWW",
+    "HSHTHSTWW",
+    "SHSTHSSSTHSSTWWW",
+    "HTHSSTHSSSWWWWWW",
+    "SHTHSTHSWW",
+    "SSSTHWWWWWW",
+    "HTHSSSTHSSW",
+    "SSTHSSWWW",
+    "HTHTHSSSTWWWWWW",
+    "HSTHSTHSSSW",
+    "HTHSTHSSSWW",
+    "HTHSTHSW",
+    "STHSTHSSSTHSSSTWWWWWWW",
+    "STHTHSTHSSWWWW",
+    "SHTHSSSTHSSTWWWWWW",
+    "HTHSHSSSTWWWWWW",
+    "SSH",
+    "SHSTHSSSTHSSTWWWW",
+    "THSHSTHSWWW",
+    "SSHW",
+    "HTHTHSSTWWWWW",
+    "THTHSHSTWWWW",
+    "SHSTHSSSTHSSWW",
+    "THSHSTHSWWWWWWW",
+    "HSSSWWWW",
+    "SSSTHSTWWW",
+    "THTHTHSWWWWWW",
+    "THSHSTHSWWWWWW",
+    "SSHWWWWWW",
+    "STHSTHSSTHSSTW",
+    "SHTHTHSSWWWW",
+    "HSTHSSSTHTWWWWWWW",
+    "THTHSHWWW",
+    "HTHTHSSWWWWWW",
+    "HSSSWW",
+    "STHSTHSSSTHSSSTWWW",
+    "STHSTHTHTWWWW",
+    "SSHTWWW",
+    "HTHSHSWWWWW",
+    "THTHSSSTHSSSWW",
+    "HSTHSSSTHSSSTWWWWWWW",
+    "SSSTHSSSTW",
+    "THSTHSSTHSSW",
+    "SSSTHSSS",
+    "SSHSWW",
+    "THTHSSTHSS",
+    "HSTHTHSSSWWWWW",
+    "SSSTHSS",
+    "SSHSWWWWW",
+    "HTHSTHSTWWWW",
+    "STHTWWW",
+    "HTHSSSWWWWWW",
+    "HSTHTHTWWWWWWW",
+    "SSSHSSSTWWWWW",
+    "SSSHSSSTWWWWWWW",
+    "SHSTHTHSTWWWWWW",
+    "HTHSHSSSWWWWWW",
+    "STHTHSTHWWWWWW",
+    "THSTHSSSTHSSSW",
+    "HTHSSSTHSWWWW",
+    "HTHSSSHSSTWW",
+    "HSTHSSTHSWWWWW",
+    "THSHSSSTHTWWWWWW",
+    "SSHWW",
+    "SSTHSSTWW",
+    "HSHSSSHSSTWWWWWW",
+    "TWW",
+    "SSHSSW",
+    "SHTHSSSTHSSWWW",
+    "SSSHSTWWWWWW",
+    "SHTHTHSSSWWWWWWW",
+    "SSHSSWW",
+    "STHSTHSTHSSWWWWWW",
+    "THTHSSTHSSSTWWW",
+    "SSSHSSSW",
+    "THTHSSSTHSWWWW",
+    "SSHSSTW",
+    "HTHSTHSSST",
+    "HWW",
+    "HSTHTHSSTW",
+    "STHSTHTHSTW",
+    "SSHSSTWW",
+    "HSHSSTHWW",
+    "SSHSTWWWWWWW",
+    "SSTHTWWWWW",
+    "THTHSSSHSSSTW",
+    "THSHSSTHSSWWW",
+    "SSSTHSWWWWWWW",
+    "HSHSTHWWWWWW",
+    "STHTHSSSTHSTWWWWWWW",
+    "THTHSSSHWWWWW",
+    "SH",
+    "HTHSSSHWWW",
+    "SSHSSTWWWWWW",
+    "THSTHSSSTHSSWW",
+    "THSHSSSTHSSWWW",
+    "SSHSSTWWWWW",
+    "HSHSSSTHTWWWW",
+    "THSHSSTHSSSTWWWWWW",
+    "STHSTHSSSTHSSWWWWWWW",
+    "SSHWWWW",
+    "STHSSWWWW",
+    "SSSTHST",
+    "THSTHSTHSTWWWWWWW",
+    "SSHSSSTWWW",
+    "HSHSTHTWWWWWWW",
+    "STHTHSSTHTW",
+    "SSHSSSTWWWW",
+    "HSTHSTHSS",
+    "SSSTHTWWWWWW",
+    "SHSSSTW",
+    "HTHSSTHSSTWWWWWWW",
+    "SSSTHSWWWW",
+    "HSHTHWWWWW",
+    "HSHTHSSWWWWWWW",
+    "STWWWW",
+    "HSSWWW",
+    "SSSTHWW",
+    "SHSTHSSTHSSSWWWWW",
+    "THTHSSSTHSSWWWWWW",
+    "SSTHWW",
+    "THSTHSSTHSSWWWW",
+    "STHSSTWWWWWW",
+    "STHSTHTHSSSTWW",
+    "SSTHSWWWWWW",
+    "SSTHWWWWWW",
+    "THTHSTHSSST",
+    "SSSTHSTWWWWW",
+    "SSSHSSWWW",
+    "THSHTHSSTWWWW",
+    "THSHSSSTHSTWWW",
+    "STHSTHSSSTH",
+    "THTHSSSTHSSS",
+    "HSHTHSSWWWWWW",
+    "SHTHTHSSWWWWWWW",
+    "THSTHTHSSTWWWWW",
+    "SSTHSTWWWWW",
+    "SSTHTWW",
+    "SSTHTWWWWWWW",
+    "HTHSHSSSTWWWW",
+    "THSHTHSSW",
+    "SSTHSWWWW",
+    "THSSSTWWW",
+    "HSTHTHSTW",
+    "THSTHTHSSTWWWW",
+    "THTHTHSSWWWW",
+    "THTHSS",
+    "SSSTHSTW",
+    "THTHSST",
+    "THSHSTHWWWW",
+    "THTHSSWWWWWWW",
+    "SSTHSTWWWWWW",
+    "SSTHSTWWWW",
+    "SSSHSS",
+    "HSHSSTHWWWWWW",
+    "SSTHSTWWWWWWW",
+    "THSHSSSTHWWWWWWW",
+    "SSTHSSW",
+    "SSTHSSTW",
+    "SSTHSSTWWWW",
+    "THSTHSSSTHSSTWWWW",
+    "THSHSSTHSSSTWWW",
+    "HTHTHSWWW",
+    "HTHSSSTHSWW",
+    "THSHSSTHSSWWWW",
+    "HTHSTHTWW",
+    "SSSW",
+    "HSHSSSTHSSTWWW",
+    "SHTHSSTHSSS",
+    "HTHSSSTHSSSWWW",
+    "SSTHSSSWW",
+    "HSHSSSHSSST",
+    "ST",
+    "SSTHSSSWWW",
+    "HSHSSSTHSSSWWWWWW",
+    "HW",
+    "HSTHTHWWWW",
+    "THTHTHSSST",
+    "THSHTHSWW",
+    "SSTHST",
+    "STHSTHSSSTHSSSWWWWWW",
+    "THSHTHSSST",
+    "THTHSSSHSSW",
+    "SSTHSSSWWWWWW",
+    "THSHSSSTHT",
+    "SSSTHSSWWWWWW",
+    "SSHSSSW",
+    "SSTHSSSTW",
+    "THTHSSTHWWWWWW",
+    "STHTHSSSTHSWWWWWWW",
+    "THSHSTHWW",
+    "SSTH",
+    "HTHSSSHSS",
+    "SSTHTWWWWWW",
+    "SSSHSTWW",
+    "STHTHSSSTHSST",
+    "SSTHSSSTWWWWW",
+    "HSHSSSTH",
+    "SHTHTHSSSTWWWWWW",
+    "SSSWWW",
+    "HSHSSSHTWWWWWW",
+    "THSHSSSTHTWWW",
+    "SSSWWWWW",
+    "THSTHSSTHTW",
+    "THSHSSSTHSSSWW",
+    "THTHSHWWWW",
+    "HTHSSTHSSSTWWW",
+    "SHTHSTHSSWWWWWWW",
+    "SSSTHSW",
+    "SSSWWWWWW",
+    "HTHSSSHWWWW",
+    "THSSTWWWWW",
+    "HTHSSSHSSTWWWWWWW",
+    "THSHSSSTHSTW",
+    "SSHSTWWW",
+    "SSSHW",
+    "HTHSSSHSSTWWW",
+    "HSTHSSTHSSSTW",
+    "STHTHSTHSSS",
+    "SSTHW",
+    "SSSHTWWW",
+    "THTHSTHSWWWWWW",
+    "SHTHSTHSSS",
+    "THSHSTHST",
+    "STHSTHTHSSTWW",
+    "SHTHTHS",
+    "HSSWWWW",
+    "SSWWWWWW",
+    "SSSHS",
+    "THTHSHSST",
+    "HTHSSTHSSSTW",
+    "SSTHSSWWWWWW",
+    "SSSHSWWWWW",
+    "SSHSSSWW",
+    "SSHSTW",
+    "HTHSSTHSSWWWWWWW",
+    "THTHWWWWWW",
+    "SSSHSTWWWWW",
+    "HTHSSTHSTWWWWWWW",
+    "HSTHSSSHTWWWW",
+    "THSTWWW",
+    "SHSTHSSSTHSSST",
+    "SSSHSSS",
+    "SSSTHWWW",
+    "SSTHSSSTWWWWWW",
+    "SSHSSTWWWW",
+    "SSSHSSSTWWWWWW",
+    "HSTHSTHSSSWWWWWWW",
+    "HSTHSSSTHSSSTW",
+    "SHSTHSSSTHSTW",
+    "SSSHWWW",
+    "SSSHSSWWWWW",
+    "SSSTWW",
+    "SSSTHSSSW",
+    "SSHSWWWWWWW",
+    "STHSTHSSSTHTWWW",
+    "THTHSTHTWW",
+    "HSHSSTHTWW",
+    "THTHSSWWWWWW",
+    "SSSHSSTWWWWW",
+    "THTHSSSTHSW",
+    "SSSHSSTWWWWWWW",
+    "THSTHSTHST",
+    "HSTHTHSSSTWW",
+    "THSHTHWWWWW",
+    "STHSTWWWWWW",
+    "IWWWWW",
+    "THSTHSSSHSSSTWWWWWW",
+    "SSSHSSSWWWWW",
+    "THSHSTHSSTWWW",
+    "STHSTWWWW",
+    "STHTHSSTHST",
+    "SSTW",
+    "SHTHSSTHTWWW",
+    "HSHSTHSSTW",
+    "SSSTHSWWWWWW",
+    "THSHSSSTHSST",
+    "STHTHSSTHTWWWW",
+    "SHSTHSSTHWWWWWWW",
+    "SSSHSSSTW",
+    "HSHSSSTHSST",
+    "HSTHSSSHTWWWWW",
+    "THSHSSTHS",
+    "SSSHSSSTWWW",
+    "THSHTHSTWWWW",
+    "SSSHSSWWWW",
+    "THSTHSSSTHSTWWW",
+    "HSHSSSTHSTWWWWWW",
+    "SSHSSWWWWWWW",
+    "SSTHWWWW",
+    "SSSTH",
+    "SSSTW",
+    "SSSTWWW",
+    "HSHTHSSTWWWW",
+    "HTHSTHSST",
+    "STHSTHSSTHSSSWWWWWWW",
+    "SSSTHWWWWWWW",
+    "THSTHSSSTHSSTW",
+    "SSSTWWWWWWW",
+    "THTHSHSWWWWWW",
+    "HTHTHT",
+    "SSSTHTW",
+    "HTHSSSTHSTWWWWW",
+    "HTHSTHT",
+    "HSHSSTHSSWWW",
+    "SSSTHTWW",
+    "SSSTHTWWW",
+    "THSTHSTHSSSWWW",
+    "THSHSSSTHSSSTW",
+    "HSTHSSTHTWWW",
+    "HSTHTHSSSWWWW",
+    "HSHTHSTWWWW",
+    "SSSTHTWWWWW",
+    "STHTHSSTHSWWW",
+    "HSHSTHSW",
+    "HSHSTHWWWW",
+    "THTHSSTHSTWWWWW",
+    "HTWWWWWWW",
+    "HTHSTHSSSTWWWW",
+    "SHTHSTHSTWWW",
+    "HSHSSSTHT",
+    "HSTHTHTW",
+    "THSTHTHTWWWWWWW",
+    "SSSTHSWWW",
+    "HSTHTHSSTWWWWW",
+    "HSTHSSSTHSSWWW",
+    "HSHSTHSWWWWWW",
+    "HSHSTHSWWWWWWW",
+    "HSHSTHST",
+    "THSSWW",
+    "HSHSSTHSWW",
+    "STHTHSSSTHST",
+    "HSHSTHSTW",
+    "HSHSTHSSSWWW",
+    "HSHSTHSTWW",
+    "THTHSTHWWWWW",
+    "HSTHTHSSWWW",
+    "HSHSTHSTWWW",
+    "HSTHSTHSSSWWWWWW",
+    "HSHSTHSTWWWW",
+    "SST",
+    "HSHSTHSTWWWWW",
+    "HSHSTHSS",
+    "THTHTHSSWWW",
+    "HSHSTHSSWW",
+    "SHSTHTHWWWWWWW",
+    "HSHSSSHSTWWWWWW",
+    "HSHSSSHSWW",
+    "THSTHSSTHWWWWWWW",
+    "HTHSTHWWWWW",
+    "THSHTHSTWWW",
+    "HSTHSTHW",
+    "STHSTHTHTW",
+    "SSHSSSTWWWWWWW",
+    "HSHSTHSSWWWW",
+    "HSHSSSHWWWWWW",
+    "HSHSTHSSWWWWW",
+    "HSHSTHSSWWWWWW",
+    "HSTHSSTHSSSWWWW",
+    "THSTHSSSHSSWWWWW",
+    "THTHSHSWWWWWWW",
+    "HSHSTHSST",
+    "HSTHSSSTHSWWWWWWW",
+    "HSHSTHSSTWW",
+    "HSHSTHSSTWWWWWW",
+    "HSHSTHSSSW",
+    "THSTHSSTHSWWWWWW",
+    "THTHTHWWWWWW",
+    "SWWWW",
+    "THTHSSSHSTWWWWWWW",
+    "SSSHTWWWWWWW",
+    "HSHSTHSSSWWWWWW",
+    "HSHTHSS",
+    "HSHSTHSSSTW",
+    "HSHSTHSSSTWW",
+    "HSHSTHSSSTWWWW",
+    "HSHSTHSSSTWWWWWW",
+    "HSHSTHSSSTWWWWWWW",
+    "HSTHTHSST",
+    "HSHSSTHW",
+    "HSHSSTHWWWW",
+    "THSTHTHSTWWW",
+    "HSHSSTHWWWWW",
+    "STHTHSSSTHTWWW",
+    "HSHSSTHWWWWWWW",
+    "HSTHSSSHTWWWWWW",
+    "THTHTHSSTWWWWWW",
+    "THTHSTHSSSWW",
+    "HSHSSTHT",
+    "THSHSSSTHSSSWWWW",
+    "STHTHSTHTWWW",
+    "THSTHSTHTWWWWWWW",
+    "HSHSSTHTW",
+    "HSHSSTHTWWWW",
+    "THTHSSSHTWWWW",
+    "HSHSSTHTWWWWW",
+    "THTHSTHSTWWW",
+    "SSSTHSWWWWW",
+    "HSHSSTHTWWWWWWW",
+    "STHTHSSTHSSSWWW",
+    "STHT",
+    "THSHSTHSTWWWWWW",
+    "HSHSSTHS",
+    "HSTHSTHSWWW",
+    "HSHSSTHSWWWW",
+    "HSHSSTHSWWWWW",
+    "HSSWWWWWW",
+    "HSHSSTHSWWWWWW",
+    "HSHSSTHSWWWWWWW",
+    "HSHSSSTHSSSWWWWWWW",
+    "THSTHSSSTHSSSTWWW",
+    "HTHSTHTWWWWWW",
+    "STHWWW",
+    "THTHTHSTWWWWWW",
+    "HSHSSTHSTWW",
+    "HTHSSWWWWWW",
+    "THTHSHSSSTWWWW",
+    "HSHTHSSW",
+    "THTHSSSHSSSWWWWW",
+    "HSHSSTHSTWWW",
+    "STHTHTHSTWWW",
+    "THSHSSSTHSSTWW",
+    "HSHSSTHSTWWWWWWW",
+    "HSHSSTHSS",
+    "HSHSSTHSSSTWWW",
+    "HSHSSTHSSW",
+    "HSHSSTHSSWW",
+    "SHSTHTHSSWWWWWWW",
+    "SSSHWWWWW",
+    "HSHSSTHSSWWWWW",
+    "HSHSSTHSSWWWWWW",
+    "HSTHSSSH",
+    "THSSSWW",
+    "THTHSSST",
+    "HSSSWWWWWWW",
+    "HSHSSTHSSWWWWWWW",
+    "THTHSSTHST",
+    "HSHSSTHSSTWW",
+    "THSTHSTHSSSTWWWWW",
+    "THSHSSTHSTW",
+    "SHTHSSSTHTWWWWW",
+    "HSHSSTHSSTWWW",
+    "HSHSSTHSSTWWWWWW",
+    "STHTHSSSTHSSWWWWWWW",
+    "SHSTWWWWWWW",
+    "HSHSSTHSSTWWWWWWW",
+    "STHTHTHSSSTWWWWW",
+    "HSTHSSTHWWWWWW",
+    "THTHSTWWWWW",
+    "THTHSSTHTWWWW",
+    "HSHSSTHSSS",
+    "HSHSSTHSSSW",
+    "STHSTHSSTHSTWWWW",
+    "HSHSSSHSTWWW",
+    "HSTHSTHWWWWWWW",
+    "THSTHSSSTHSSSTWWWWWWW",
+    "HSTHSSSHSSWWWWWWW",
+    "THSHSTHSSSTWWW",
+    "STHSTHSSTHS",
+    "HSHSSTHSSSWW",
+    "HSHSSTHSSSWWWW",
+    "THSHSSSTHTWWWWW",
+    "HSHSSTHSSST",
+    "STHTHSSSTHSSSW",
+    "HTHSSSHSWWWW",
+    "HSHSSSTHSWWW",
+    "HSHSSTHSSSTWW",
+    "HSTHSTHSST",
+    "HSHSSTHSSSTWWWWWW",
+    "SSSHWWWW",
+    "THSHSSTHSST",
+    "HSHSSTHSSSTWWWWWWW",
+    "HSHSSSH",
+    "HSHSSSHWW",
+    "SHSTHSSTHSSTWW",
+    "HSTHSSSHSTWWW",
+    "HSHSSSHWWW",
+    "HSHSSSHWWWW",
+    "HSHSSSHWWWWW",
+    "STHTHTHSSSWWWWWWW",
+    "THSHSSSTH",
+    "THSTHSSSTHSWWWWWW",
+    "HSHSSSHT",
+    "HSHSSSHTWWW",
+    "THTHSSSHSWW",
+    "HSHSSSHTWWWW",
+    "HSHSSSHTWWWWW",
+    "SHSTHTHSSSTWWWWWW",
+    "HSHSSSHTWWWWWWW",
+    "HSHSSSHSWWW",
+    "HSHSSSHSWWWW",
+    "HSHSSSHSWWWWW",
+    "THSTHSTHSSWWW",
+    "HSTHTHSWWWWW",
+    "SHTHSTHSSSWWWW",
+    "THSSTWWWWWW",
+    "HSHSSSHSWWWWWW",
+    "HSHSSSHSWWWWWWW",
+    "SHSTHTHSSSWWWW",
+    "THTHSSSHSSSWW",
+    "HSHSSSHSTWW",
+    "THSTHSSTHSSTWWW",
+    "THTHSSTHW",
+    "THSHSSTHSSSWWW",
+    "HTHTHWWWWWW",
+    "HSTHSSSTHTWWW",
+    "HSHSSSHSTWWWWWWW",
+    "THTHSSTHSSTWWWWWW",
+    "THTHSTHSSSTWWWW",
+    "HSHSSSHSS",
+    "HSHSSSHSSW",
+    "HSHSSSHSSWWWW",
+    "THSHSSTHSSSWWWWWWW",
+    "STHTHSTHSSWWWWW",
+    "HSHSSSHSSWWWWW",
+    "THTHSSSTHWWWWW",
+    "HSHSSSHSSWWWWWWW",
+    "HTHSSSTHSSTWWWWWW",
+    "HSHSSSHSSTWW",
+    "THTHSHSSTW",
+    "HSTHSTHTWWWWWW",
+    "HSHSSSHSSTWWWWWWW",
+    "STHSTHSSSTHSSTW",
+    "SHSTHTHSSW",
+    "HSHSSSHSSS",
+    "SHTHSTHSTWW",
+    "HSHSTHSWWWWW",
+    "THSHTHSS",
+    "THSHSSTHTWWW",
+    "SWWWWW",
+    "HSHSSTHSTWWWW",
+    "HSHSSSHSSSW",
+    "HSHSSSHSSSWWW",
+    "HSHSSSHSSSWWWWW",
+    "THTHSHTWWWW",
+    "HSHSSSHSSSWWWWWW",
+    "IWW",
+    "HSHSSSHSSSWWWWWWW",
+    "SHTHSSSTHSSSTWWWWWWW",
+    "HSHSSSHSSSTW",
+    "THSHTHSSSWWW",
+    "HSHSSSHSSSTWW",
+    "HSHSSSHSSSTWWWW",
+    "THSHSTHSSWW",
+    "HSHSSSHSSSTWWWWW",
+    "THSTHSSSTHSW",
+    "HSTHTHSSSTWWWWW",
+    "HSHSSSHSSSTWWWWWW",
+    "HSHSSSHSSSTWWWWWWW",
+    "HSHSSSTHW",
+    "THSTHTHSSSW",
+    "HSTHSTHSTWWWWWWW",
+    "HSHSSSTHWWWWWW",
+    "SSTHSSTWWWWWWW",
+    "HSHSSSTHTW",
+    "HSHSSSTHTWWWWW",
+    "THTHSHSSWWWWW",
+    "HSHSSSTHTWWWWWW",
+    "STHTHSTHSSSWW",
+    "HSHSSSTHSSWW",
+    "THTHSSSTWWWWWW",
+    "HSHSSSTHSWW",
+    "HSHSSSTHSWWWW",
+    "HSHSSSTHSWWWWW",
+    "THTHSSSTHWWWWWWW",
+    "HTHSSSTHTWW",
+    "HSHSSSTHSWWWWWW",
+    "HSTHSSSTHSSSW",
+    "THSWWW",
+    "HSHSSSTHSTW",
+    "THSTHSTHTWWWWW",
+    "THTHSSTHWWWWWWW",
+    "THTHSSTHSSTWWW",
+    "HSHSSSHTW",
+    "HSHSSSTHSTWWWW",
+    "HSHSSSHSSTWWW",
+    "SSSWWWWWWW",
+    "THTHSHSSWWWWWW",
+    "HSHSSSTHSTWWWWW",
+    "HSHSSSTHSTWWWWWWW",
+    "THSTHSSTHSSTWWWWWW",
+    "SHW",
+    "HSHSSSTHSS",
+    "HTHSHSSTWW",
+    "HSHSSSTHSSW",
+    "HSHSSSTHSSWWW",
+    "HSHSSSTHSSWWWW",
+    "THTHS",
+    "THTHSH",
+    "THSTHSSSHSSWWW",
+    "HSHSSSHSSTWWWWW",
+    "HSHSSSTHSSWWWWW",
+    "HTHSSSHSSSWW",
+    "HSTHSSSTHSWWWWW",
+    "HSHSSSTHSSWWWWWW",
+    "THTHSSSHSTWWWWW",
+    "HSHSSSTHSSTW",
+    "HSHSSSTHSSTWW",
+    "HSHSSSTHSSTWWWW",
+    "HSHSSTHSSSWWWWWWW",
+    "HSHSSSTHSSTWWWWW",
+    "THSTHSSSHSSW",
+    "THSHSSTHT",
+    "THTHTHSSWW",
+    "HSHSSSTHSSTWWWWWW",
+    "THSTHTHSSSWWWWWWW",
+    "HSTHSSTHSSSWWWWWW",
+    "HSHSSSTHSSTWWWWWWW",
+    "HSHSSSTHSSS",
+    "SHTHSSSTHSSSTWW",
+    "HSHSSSTHSSSW",
+    "STHSTHSSSTHSTWW",
+    "THSHSSSTHSTWWWWW",
+    "HSHSSSTHSSSWWWW",
+    "THSHTHWWW",
+    "HSHSSSTHSSSWWWWW",
+    "THTHTHSSSTWW",
+    "SHTHSSSTHSSWWWWW",
+    "HSHSSSTHSSST",
+    "THTHTHW",
+    "HSHSSSTHSSSTW",
+    "SSSTHSTWW",
+    "THSHSSSTHST",
+    "HSHSSSTHSSSTWW",
+    "HTHSWW",
+    "HSHSSSTHSSSTWWWWW",
+    "SHSTHSTHTWWWWW",
+    "HSHSSSTHSSSTWWWWWW",
+    "HSHSSSTHSSSTWWWWWWW",
+    "SHTHSSTHSS",
+    "THSHSSTHWWWWW",
+    "THSHSSSTHTW",
+    "HSTHTHSSWW",
+    "HSTHTHWW",
+    "HSTHTHWWW",
+    "THTHSSSHSSSWWWWWW",
+    "STHSTHSTHSSWW",
+    "HSTHTHT",
+    "HSTHSSTHSST",
+    "HSTHTHTWW",
+    "HSTHSSSTHWWW",
+    "HSTHTHS",
+    "HSTHTHSW",
+    "HSTHTHSWW",
+    "THTHSSTHSSSTWWWWWW",
+    "SSSTHSTWWWW",
+    "HSTHTHSWWWWWWW",
+    "HSTHTHST",
+    "HSTHTHSTWW",
+    "HSTHTHSTWWW",
+    "HSTHTHSTWWWWW",
+    "HSTHTHSTWWWWWW",
+    "THTHSSSTHSSSTWWW",
+    "THSTHSTHSSSWWWWWWW",
+    "THSTHTHT",
+    "SSSHSSTWWWWWW",
+    "HSTHTHSTWWWWWWW",
+    "HSTHTHSSW",
+    "SHSTHSSSTHSSSWW",
+    "HSHTHSW",
+    "HSTHTHSSWWWW",
+    "HSTHTHSSWWWWWWW",
+    "THSHTHTW",
+    "HSTHTHSSTWWW",
+    "HSTHTHSSTWWWW",
+    "STHTHSSSTHSSTWWWWWWW",
+    "HSTHTHSSTWWWWWWW",
+    "THSTHSSSHTW",
+    "HSTHTHSSS",
+    "HSTHTHSSSW",
+    "HSTHTHSSSWW",
+    "SSTHSS",
+    "SSTWWWW",
+    "HSTHTHSSSWWWWWWW",
+    "HSTHTHSSSTW",
+    "HSTHTHSSSTWWW",
+    "HSTHSTH",
+    "HSTHSTHWWW",
+    "HSTHSTHWWWW",
+    "THSTHSSSHWWW",
+    "HTHSSSTHSSSTWW",
+    "HTHSHSTW",
+    "HSTHSTHT",
+    "SHSTHSTHWW",
+    "HSTHSTHTW",
+    "HSTHSTHTWW",
+    "HSTHSTHTWWW",
+    "HSTHSSSTHSSSTWWW",
+    "THSTHSSSHSSTWW",
+    "HSTHSTHTWWWW",
+    "THSHSSSTHSSSTWWWWW",
+    "HSTHSTHTWWWWW",
+    "THTHSSSHSSTWWWW",
+    "THTHSSTHSSWWW",
+    "HSTHSTHSW",
+    "HSTHSTHSWW",
+    "HSTHSTHSWWWWWW",
+    "THTHSHSSWWWW",
+    "HSTHSTHSWWWWWWW",
+    "HSTHSTHST",
+    "HSHSTHWWWWWWW",
+    "HSTHSTHSTW",
+    "THSTHSSSHSWWWWW",
+    "HSTHSTHSTWW",
+    "HSTHSTHSTWWW",
+    "SSSTHTWWWW",
+    "HSTHSTHSTWWWWW",
+    "HSHTHSSSTWWWWW",
+    "THSHSSSTHSWWWW",
+    "HSTHSTHSTWWWWWW",
+    "HSTHSTHSSW",
+    "HSTHSTHSSWW",
+    "HSTHSTHSSWWWW",
+    "THSHSSSTHTWWWW",
+    "SHSTHSSTHSSTWWW",
+    "SSTHSSSWWWW",
+    "HSTHSTHSSWWWWW",
+    "THSTHSSSTHSWWWW",
+    "HSTHSTHSSWWWWWW",
+    "HSTHSSTHT",
+    "THTHSSSTHS",
+    "HTHSSSHSSWWWWWWW",
+    "THSHSTHSSSTWWWW",
+    "HSTHSTHSSTW",
+    "THSHSTHSTWWWW",
+    "THTHSSSTH",
+    "HSTHSTHSSTWWW",
+    "THSHSTHWWW",
+    "SHSTHSTHSSSW",
+    "HTHTHSTWWWWW",
+    "HSTHSTHSSTWWWW",
+    "SHSTHSSTHST",
+    "THSTHSTHSTW",
+    "THTHSSSTHSSSWWW",
+    "HSTHSTHSSSWW",
+    "HSTHSTHSSSWWW",
+    "HSHTHSWWW",
+    "HSTHSSTHSSSTWWWW",
+    "THTHSTHSSTWWWWWWW",
+    "THTHSSTHSST",
+    "THSHSSSTHWWW",
+    "HSTHSTHSSSWWWWW",
+    "STHSTHSSTHSSS",
+    "HSTHSTHSSSTW",
+    "THSTHSSTHW",
+    "HSTHSTHSSSTWW",
+    "HSTHSTHSSSTWWW",
+    "HSTHSTHSSSTWWWWWWW",
+    "STHTHSSSTHSS",
+    "HSHSTHSSTWWWWW",
+    "HSTHSSTH",
+    "THSTHSSSTHSTWWWWWWW",
+    "HSHSTHSSWWW",
+    "HSTHSSTHW",
+    "SHSSSWWWW",
+    "THTHSSTWWWWW",
+    "HSTHSSTHWW",
+    "THSTHSSSTHTWWWWWW",
+    "THTHSSSHSSWWW",
+    "HSTHSSTHWWWWW",
+    "STHSTHTHSWW",
+    "THTHTHSSWWWWWW",
+    "HSTHSSTHWWWWWWW",
+    "THSHSSSTHW",
+    "HSTHSSSHSSTWWW",
+    "HSTHSSTHTWWWW",
+    "THTHSSTHSSTWW",
+    "THTHSTHSTWW",
+    "THTHSSTWWW",
+    "HSTHSSTHTWWWWW",
+    "HSTHSSTHSTWWWWW",
+    "HSTHSSTHTWWWWWW",
+    "THTHSSSWWWW",
+    "HSTHSSTHSWWWW",
+    "HSTHSSTHSWWWWWW",
+    "SHTHSSSTHSSSWWWWW",
+    "SSSHTWWWWWW",
+    "HSTHSSTHSWWWWWWW",
+    "HSTHSSSHST",
+    "STHTHSSTHSSSTWWWWWWW",
+    "THSTHTHST",
+    "HTHSSSTHSSTWWWWW",
+    "HSTHSSTHSTW",
+    "HTHSSTHSSSTWWWWWWW",
+    "THSHTHSSTWWWWWW",
+    "STHTHSTHSW",
+    "HSTHSSTHSTWWW",
+    "HSTHSSTHSSTWWW",
+    "SHSTHTHSSSTWWW",
+    "HSTHSSSHSSTWWWWW",
+    "STHSSS",
+    "HSTHSSTHSTWWWWWW",
+    "HSTHSSTHSTWWWWWWW",
+    "HSTHSSTHSS",
+    "STHSTHSSTHWWWWW",
+    "SHSTHSTHWWWWWW",
+    "HSTHSSTHSSWW",
+    "HSTHSSTHSSWWWWW",
+    "HSTHSSTHSSWWWWWW",
+    "THTHSHSTWW",
+    "HSTHSSTHSSWWWWWWW",
+    "HSTHSSTHSSTW",
+    "HSTHSSTHSSTWW",
+    "THSTHSSSTHSWWWWW",
+    "SSWWWWW",
+    "HSTHSSTHSSTWWWW",
+    "STHSTHSTHSSSW",
+    "HSTHSSTHSSTWWWWW",
+    "HSTHSSTHSSTWWWWWW",
+    "STHTHSTHSWWWWWW",
+    "HSTHSSTHSSS",
+    "HSTHSSTHSSSWWW",
+    "SSSTHSSWWWW",
+    "THTHSTHSTWWWWWW",
+    "STHSTHSSSTHSTW",
+    "THTHSHSW",
+    "SHWWW",
+    "HSTHSSTHSSSWWWWW",
+    "HSTHSSTHSSST",
+    "SHTHSSTHSST",
+    "THTHTHWWWWWWW",
+    "SSSTHSSSWWWWWWW",
+    "HSTHSSTHSSSTWWW",
+    "HSTHSSTHSSSTWWWWW",
+    "THWW",
+    "HSTHTH",
+    "HSTHSSSHWW",
+    "HSTHSSSHWWW",
+    "HSTHSSSHWWWW",
+    "SSSHTWWWW",
+    "HSTHSSSHWWWWW",
+    "HSTHSSSHWWWWWW",
+    "THSHSSTHWWWWWWW",
+    "HSTHSSSHWWWWWWW",
+    "SHTHTHTWWW",
+    "THSHSTHSSSW",
+    "HSTHSSSHT",
+    "HSTHSSSHTW",
+    "SSHSWWWWWW",
+    "THSSSTWWWWW",
+    "HSTHSSSHTWW",
+    "HSTHSSSHTWWW",
+    "SHTHTHSWWWWWW",
+    "HTHSSSHSSTWWWWW",
+    "HSTHSSSHS",
+    "STHSTHSTH",
+    "HSWWWW",
+    "HSTHSSSTHWWWWW",
+    "HSTHSSSHSWW",
+    "HTHSSSWWWW",
+    "THTHSSTHSSW",
+    "HSTHSSSHSWWW",
+    "HSHSSSHS",
+    "SSSHSW",
+    "HSTHSSSHSWWWW",
+    "HSTHSSSHSWWWWWW",
+    "HTHSHS",
+    "HSTHSSSHSTWWWWW",
+    "HSTHSSSHSTWWWWWW",
+    "HSTHSSSHSTWWWWWWW",
+    "STHSTHSSSTHSSSWWWWWWW",
+    "HTHTHSWWWW",
+    "HSTHSSSHSSWW",
+    "HSTHSSSTHSTWWWW",
+    "THTHSSSTHSTWWWWWW",
+    "STHSTHSSSTHSSWWW",
+    "HSTHSSSHSSWWW",
+    "SS",
+    "HSTHSSSHSSWWWW",
+    "HTHSSSTHSWWW",
+    "HTHSTH",
+    "HSTHSSSHSST",
+    "HSTHSSSHSSTW",
+    "SHSTHTHWWWWW",
+    "HSHSSTHSSSTWWWWW",
+    "HSTHSSSHSSTWWWW",
+    "STHSTHTHSSST",
+    "SHTHSSSTHSTW",
+    "HSTHSSSHSSTWWWWWW",
+    "STWW",
+    "THTHSSSTHSSST",
+    "HSTHSSSHSSS",
+    "THSHTHTWWWW",
+    "THTHSSSHSSSWWW",
+    "HTHSHSSWWWW",
+    "HSTHSSSHSSSW",
+    "HSTHSSSHSSSWW",
+    "HSTHSSSTHWW",
+    "STHSSW",
+    "HSTHSSSHSSSWWWWW",
+    "HSTHSSSHSSSWWWWWW",
+    "THTHSSSHSSWWWWWW",
+    "HSTHSSSHSSST",
+    "SWWWWWW",
+    "THTHSHSSTWWWW",
+    "SSSHSSSWWW",
+    "HSTHSSSHSSSTW",
+    "HTHSSTHSSTWWWW",
+    "THTHSSSTHT",
+    "HSTHSSSHSSSTWWW",
+    "HSTHSSSHSSSTWWWW",
+    "HSTHSSSHSSSTWWWWW",
+    "HSTHSSSHSSSTWWWWWW",
+    "THSTHTHSTWWWWW",
+    "HSTHSSSTH",
+    "HSTHSSSTHWWWW",
+    "HSW",
+    "THTHSSTHTWW",
+    "SHSTHSSSTHW",
+    "THTHSSSHTWWWWWWW",
+    "THTHSSSTHTWWWWWWW",
+    "HSTHSSSTHWWWWWW",
+    "STHSWWWWWWW",
+    "THSHSSTHSWWWWWWW",
+    "HSTHSSSTHT",
+    "THSTHSSSHSWWWWWWW",
+    "THTHSSTHSSWWWWWW",
+    "HSTHSSSTHTWW",
+    "HSTHSSTHSTWWWW",
+    "HSTHSSSTHTWWWW",
+    "THTHSSTHTWWW",
+    "SSTHSSWWWWW",
+    "HSTHSSSTHTWWWWW",
+    "THSHSTHSSSWWWWW",
+    "THSHSSTHSSTWWWW",
+    "STHTHSTHWWWWW",
+    "THSHSTHSSTWW",
+    "HSTHSSSTHTWWWWWW",
+    "HSTHSSSTHSWWW",
+    "HSTHSSSTHSWWWW",
+    "HTHSSTHSW",
+    "THTHSHTWWWWWW",
+    "HTHSSSTHSSSWWWWW",
+    "THSHSSTHSSSWWWW",
+    "SSTWWW",
+    "HSTHSSSTHSWWWWWW",
+    "SHSTHTHSSS",
+    "HSTHSSSTHST",
+    "SHSTHSSTHSSWWWW",
+    "HSTHSSSTHSTW",
+    "THSTHSSTHWWW",
+    "SSSTHS",
+    "HSTHSSSTHSTWW",
+    "THTHSTHSTW",
+    "STHSTHSSTHSWWW",
+    "HSTHSSSTHSTWWW",
+    "THSSST",
+    "HSTHSSSTHSTWWWWW",
+    "HSTHSSSTHSTWWWWWW",
+    "HSTHSSSTHSTWWWWWWW",
+    "THTHSTWWWW",
+    "THTHSSSTHSSTWWWWWW",
+    "HSTHSSSTHSSW",
+    "HTHTWWW",
+    "HSTHSSSTHSSWWWWWWW",
+    "HSTHSSSTHSST",
+    "THSHSSTHTWWWWWWW",
+    "HSTHSSSTHSSTW",
+    "HTHSHSTWWW",
+    "HSTHSSSTHSSTWW",
+    "THTHSSSHSSSTWWWWW",
+    "THTHTHT",
+    "SHTHSSSTHWWWWW",
+    "HSTHSSSTHSSTWWWWWW",
+    "HSTHSSSTHSSSWW",
+    "HSTHSSSTHSSSWWWW",
+    "HSTHSSTHSSWWWW",
+    "HSTHSSSTHSSSWWWWWW",
+    "HSTHSSSTHSSSWWWWWWW",
+    "HSTHSSSTHSSSTWWWWW",
+    "THTHSTHWWWWWW",
+    "HSHSSSTHWWWWWWW",
+    "THSHSSTHSWWW",
+    "HSTHSSSTHSSSTWWWWWW",
+    "SHSTHSTHSSWWWWW",
+    "THTHW",
+    "SSHTWWWWW",
+    "HSHSSTHST",
+    "THSHSSSTHWWWWWW",
+    "THTHWW",
+    "SHSTWWWWWW",
+    "THTHSSSTHSSSTW",
+    "THTHWWW",
+    "THTHWWWW",
+    "THTHTW",
+    "STHSTHTHSTWWWWW",
+    "SHSTHSSTHSSSW",
+    "THSTHTHSSTWWW",
+    "THTHTWW",
+    "THTHTWWWW",
+    "HSHSTHSTWWWWWWW",
+    "THSHSTHSWW",
+    "THSHSTHSSTWWWWW",
+    "THTHTWWWWWWW",
+    "THTHSTHSSSTWWWWWWW",
+    "HTHSWWWW",
+    "THTHTH",
+    "THTHTHWWW",
+    "THTHTHWWWWW",
+    "THTHTHTW",
+    "THTHTHTWW",
+    "THTHTHTWWW",
+    "THTHTHTWWWWWW",
+    "HTHSHSSSTWWW",
+    "THTHSHSWWWWW",
+    "THTHTHSW",
+    "STHTHTHSTWW",
+    "THTHSSSHTWWWWW",
+    "THTHTHSWW",
+    "THTHTHSWWWW",
+    "THTHTHSWWWWW",
+    "STHSSWW",
+    "THTHTHST",
+    "SHSTHSSTHW",
+    "THTHTHSTW",
+    "HSHSSSHSTWWWW",
+    "THTHTHSTWW",
+    "THTHTHSTWWW",
+    "THTHSTHWWW",
+    "STHTHTHSSTWWWWWW",
+    "THTHTHSTWWWW",
+    "THTHTHSTWWWWW",
+    "THTHTHSS",
+    "THTHSHSSSTWW",
+    "STHTHTHSSTW",
+    "THTHTHSSW",
+    "THSTHTHSSST",
+    "THTHTHSSSTWWWWWWW",
+    "SHSTHTHSSSTWW",
+    "THTHTHSSWWWWW",
+    "THTHTHSST",
+    "THTHSTHSSWW",
+    "THTHTHSSTW",
+    "STHTHSSSTHSSSTWWWW",
+    "THSHTHSSWW",
+    "THSHSSTHSSSTW",
+    "THTHTHSSTWW",
+    "THTHTHSSTWWWW",
+    "THTHTHSSTWWWWW",
+    "THTHTHWW",
+    "THTHTHSSSW",
+    "HSTHSSSTHSW",
+    "THTHSTHSSTWWW",
+    "THTHTHSSSWWWW",
+    "THSHTHSTWW",
+    "HSTW",
+    "THTHTHSSSWWWWWWW",
+    "HSHSSSTHSWWWWWWW",
+    "THTHTHSSSTWWWWW",
+    "HSHSSSHSSTWWWW",
+    "THTHTHSSSTWWWWWW",
+    "THTHSW",
+    "HWWWWWW",
+    "THTHST",
+    "SSSTHSSTWWWWWWW",
+    "THTHSWWW",
+    "THSTHSTHSSTWWWWWWW",
+    "THTHSWWWW",
+    "THTHSWWWWW",
+    "SHSTHSSSTHWWW",
+    "THTHSWWWWWW",
+    "SHSTHSSSTHSTWW",
+    "THSTHTHSSSTWWWWW",
+    "THTHSWWWWWWW",
+    "THSHTHSSSTWW",
+    "STHSTHSTHSWW",
+    "HSTHSTHWWWWWW",
+    "THTHSHW",
+    "THTHSHWW",
+    "THTHSHWWWWW",
+    "THTHSHWWWWWW",
+    "THTHSHT",
+    "SHTHSSTHSSTWWWWW",
+    "THTHSHTW",
+    "STHSSST",
+    "THTHSHTWW",
+    "HTHSSSTWWWWW",
+    "THTHSHTWWW",
+    "HTHSHSSTWWWWW",
+    "THTHSHTWWWWW",
+    "THTHSHTWWWWWWW",
+    "THTHSHS",
+    "HTHTHS",
+    "THTHTHTWWWW",
+    "THTHSHSWWW",
+    "THTHSHSWWWW",
+    "HTHSHSSSWWWW",
+    "THTHSHSSSWWWWWWW",
+    "HTHSTHSSTWWWWW",
+    "THTHSHST",
+    "STHSTHSSTHTWWWW",
+    "HTHSSSHSSWWWWWW",
+    "THTHSHSTWWWWW",
+    "THTHSHSTWWWWWW",
+    "SHTHSSTHSSSTWWWWWWW",
+    "THTHSHSTWWWWWWW",
+    "THSTHSSSHSWWW",
+    "THTHSTHSSS",
+    "THTHSSTHSSSTWW",
+    "THTHSHSSW",
+    "THTHSHSSSTWWWWW",
+    "SSSTHWWWW",
+    "THTHSHSSTWWWWW",
+    "SHTHSTHSSSTWWW",
+    "SSHSW",
+    "SSTHSWWWWW",
+    "THTHSHSSS",
+    "SHTHTHSSTWWWWW",
+    "THTHSHSSSWW",
+    "THTHSHSSSWWW",
+    "THTHSHSSSWWWW",
+    "THSTHSSSHSSST",
+    "HTHSSWWWW",
+    "THTHSHSSSWWWWW",
+    "THSTHSSTHSSTWWWWWWW",
+    "THTHSHSSSTW",
+    "HSHSSTHSSSTW",
+    "SHWW",
+    "THTHSHSSSTWWW",
+    "HSHTHSSSWWW",
+    "THTHSHSSSTWWWWWW",
+    "STHTHSSTHWWW",
+    "THSHSSSTHSTWWWW",
+    "THTHSHSSSTWWWWWWW",
+    "H",
+    "THTHSTW",
+    "THTHSTWWW",
+    "THTHSTWWWWWW",
+    "THTHSTWWWWWWW",
+    "THTHSTHW",
+    "THTHSTHT",
+    "THTHSTHTWWW",
+    "STHTHTHSSSWWW",
+    "SHSTHSTHT",
+    "THTHSTHTWWWW",
+    "THTHSSSHWWWWWWW",
+    "THTHSTHTWWWWW",
+    "STHSTHSSSTHSW",
+    "THTHSTHTWWWWWW",
+    "STHS",
+    "THTHSTHTWWWWWWW",
+    "THWWWWW",
+    "THTHSTHS",
+    "THTHSTHSW",
+    "THSHTHSSWWW",
+    "THTHSTHSWW",
+    "THSTHSSSTHSSSTWWWW",
+    "THSTHSSTHSSSWWWWWW",
+    "THTHSTHSWWW",
+    "STHSTHSTHSSTWWWW",
+    "THTHSTHSWWWWW",
+    "THTHSTHSWWWWWWW",
+    "THSHTHSSTW",
+    "THSHSSTHSSSWW",
+    "THTHSTHST",
+    "SHSSTWW",
+    "THTHSSSTHSSTWWWW",
+    "SHSTHTHSSWW",
+    "THTHSTHSTWWWW",
+    "SSSTWWWWWW",
+    "THTHSTHSS",
+    "THSTHSTHSSTWWWWWW",
+    "THTHSTHSSW",
+    "THTHSSSTWWWW",
+    "THTHSTHSSWWWW",
+    "THTHSTHSSWWWWW",
+    "STWWWWWW",
+    "THTHSTHSSWWWWWW",
+    "THTHSTHSST",
+    "THSHSSTHWWWWWW",
+    "THTHSTHSSTW",
+    "SHSTHSSSTHSSTWW",
+    "HTHTHWW",
+    "THTHSTHSSTWWWWWW",
+    "HSHSTHSSTWWWW",
+    "THTHSTHSSSW",
+    "SHSTHSTHTWWWWWW",
+    "HTHSHSSTWWWWWW",
+    "THTWWWW",
+    "HSTHSTHSSST",
+    "HSTHSSSTHSWW",
+    "THTHSTHSSSWWWWW",
+    "SHTHSSSTHSSWWWWWWW",
+    "THTHSTHSSSWWWWWW",
+    "THTHSTHSSSWWWWWWW",
+    "THTHSSTW",
+    "THTHSSTHSTW",
+    "THTHSTHSSSTWW",
+    "HSTHSSTHWWW",
+    "THTHSSSTHSWWWWW",
+    "SHSTHSTHSSWWW",
+    "THTHSTHSSSTWWW",
+    "THTHSTHSSSTWWWWWW",
+    "THSTHSSSHSTWW",
+    "SSSTHSSTWWW",
+    "HSTHSSTHSWW",
+    "THTHSSSTHSTWWWW",
+    "THTHSSWW",
+    "THTHSSWWW",
+    "THTHSSTWW",
+    "HSHSSTHSSSWWWWWW",
+    "THTHSSTWWWWWW",
+    "THTHSSTWWWW",
+    "THTHSSTHWW",
+    "STHSTHSSSTHSSST",
+    "SHSTHSSTHSSTWWWWWWW",
+    "THTHSSTHT",
+    "STHSTHTHSSWW",
+    "THTHSSSHWW",
+    "STHTHSTHSSW",
+    "HTHSSSHSWWWWWWW",
+    "SHSSTWWWWW",
+    "THTHSSTHTW",
+    "THTHSSTHTWWWWW",
+    "THTHSSTHS",
+    "THTHSSTHSW",
+    "THTHSSTHSWW",
+    "THTHSSTHSWWW",
+    "THTHSSTHSWWWWW",
+    "THTHSSTHSWWWWWW",
+    "HSTHTHSTWWWW",
+    "THTHSSTHSTWW",
+    "THSHTHSWWW",
+    "HSHSSSTHSSWWWWWWW",
+    "THSHSTH",
+    "HTHSSSTHSWWWWW",
+    "HSSTWWWWW",
+    "THTHSSTHSSWWWW",
+    "SSSHSSWWWWWW",
+    "THTHSSTHSSWWWWW",
+    "THTHSSTHSSTW",
+    "THTHSSTHSSTWWWW",
+    "THTHSSTHSSTWWWWW",
+    "STHSTHSSSTHSSWWWWWW",
+    "STHTHTHSTWWWWW",
+    "SHSTHSTHSSTW",
+    "THTHSSTHSSTWWWWWWW",
+    "THTHSSTHSSSW",
+    "THTHSSTHSSSWW",
+    "HSTHSTHSSWWWWWWW",
+    "THSHSSSTHSSWWWWWW",
+    "THTHSSTHSTWWWWWWW",
+    "THTHSSTHSSST",
+    "THTHSSTHSSSTWWWWW",
+    "THTHSSTHSSSTWWWWWWW",
+    "HTHSSSHTWWWWWWW",
+    "HTHSHSSW",
+    "THTHSSS",
+    "HTHSSSHSTWWWW",
+    "THSHSSTHSSSWWWWW",
+    "THTHSSSW",
+    "THTHSSSWW",
+    "THTHSSSWWW",
+    "THSHTHSSSW",
+    "SHTHSTHST",
+    "SSSHSSWW",
+    "THTHSSSWWWWW",
+    "HSHTHTWW",
+    "HTHSSSHW",
+    "THTHSSSWWWWWWW",
+    "THTHSSSH",
+    "THTHSSSHWWW",
+    "STHTHTHSSW",
+    "SHTHTHSSTWWW",
+    "HSHSSSHW",
+    "THSHTHWWWW",
+    "THTHSSSHWWWW",
+    "STHTHSSTHTWWWWW",
+    "HSTHTHSWWWW",
+    "THTHSSSHT",
+    "HSTHSSSHSSTWWWWWWW",
+    "THTHSSSHTW",
+    "STHTHSSTHSSSTWWWW",
+    "THSHTHSWWWWW",
+    "HTHSSSHSSTWWWWWW",
+    "THTHSSSHTWWWWWW",
+    "SSHSSSTW",
+    "THTHSSSHSW",
+    "THTHSSSHSWWW",
+    "THTHSSSHSWWWW",
+    "THTHSSSHSWWWWW",
+    "THTHSSSHSWWWWWW",
+    "THTHSSSHSWWWWWWW",
+    "THTHSSSHSTW",
+    "THSSSW",
+    "THTHSSSHSTWWW",
+    "HTHTHST",
+    "THTHSSSHSTWWWW",
+    "THTHSSSTHTWWWWW",
+    "STHSTHSSTH",
+    "STHSTHTHS",
+    "THTHSSSHSS",
+    "HSHSSSTHSTWW",
+    "HTHSHSSSTWW",
+    "THTHSSSHSSWW",
+    "STHTHSTHSTWWW",
+    "THSHSTHSSS",
+    "THTHSSSHSSWWWW",
+    "THSTHSSSTHSSWWWWWWW",
+    "THTHSSSHSSWWWWW",
+    "THTHSSSHSSWWWWWWW",
+    "SHSTHSSSTHSWWWWW",
+    "HSTHTHTWWW",
+    "THSHSTHSSSWWW",
+    "THTHSSSHSSTWW",
+    "HSSS",
+    "THTHSSSHSSTWWWWW",
+    "THTHSSSHSSTWWWWWW",
+    "SSTHSSTWWWWW",
+    "THTHSSSHSSTWWWWWWW",
+    "HTHSHSSWWWWWW",
+    "THTHSTWW",
+    "THTHSSSHSSS",
+    "THTHSSSHSSSW",
+    "HSHTHSSWWWWW",
+    "THTHSSSHSSSWWWWWWW",
+    "SHSTHTHSSSWWW",
+    "THTHSSSHS",
+    "THTHSSSTHSTWWWWWWW",
+    "THSHSTHSS",
+    "SHSTHTHSSSTW",
+    "THTHTHSSSWW",
+    "SSHSSSWWWWWWW",
+    "HTHSSSTHTWWWWW",
+    "HSTHSSSTHTW",
+    "THTHSSSHSSST",
+    "SHSTHSTHSWWWWWWW",
+    "THTHSSSHSSSTWW",
+    "THTHSSSHSSSTWWW",
+    "THTHSSSTW",
+    "HTHSTHSSWWWW",
+    "SSSTHSSSTWWWW",
+    "THTHSSSTWWWWWWW",
+    "STHTHSTHSWWWWW",
+    "HSHTHST",
+    "THTHSSSHSSSTWWWW",
+    "THTHSSSTHW",
+    "SSHWWWWWWW",
+    "THTHSSSTHWW",
+    "STHTHSSSTHSSS",
+    "STHSST",
+    "THTHSSSTHWWW",
+    "SHTHTHSSSWWW",
+    "THTHSSSTHWWWW",
+    "THTHSSSTHWWWWWW",
+    "THTHSSSTHTWWWW",
+    "HSTHSTHS",
+    "THTHSSSTHSWWWWWW",
+    "STHSTHSTHWW",
+    "THTHSSSTHSWWWWWWW",
+    "STHSTHSTHSSTWWW",
+    "HSTHTHWWWWWWW",
+    "THTHSSSTHST",
+    "SHSTHSTHW",
+    "THTHSSSTHSTW",
+    "THTHSSSTHSTWWWWW",
+    "THTHSSSTHSS",
+    "SHSTHSTHTWW",
+    "THTWWWWWWW",
+    "THTHSSSTHSSWW",
+    "THTHSSSTHSSWWW",
+    "THTHSSSTHSSWWWW",
+    "THTHSSSTHSSWWWWWWW",
+    "THTHSSSTHSSSW",
+    "STHTHSSTHSSSWWWWWWW",
+    "THTHSSSTHSSSWWWWW",
+    "HSHSTHTWWW",
+    "THTHSSSTHSSSTWW",
+    "THTHSSSTHSSSTWWWW",
+    "SHTHTHSTWWWWWWW",
+    "HTHSSSHSSSWWWWWW",
+    "THTHSSSTHSSSTWWWWWW",
+    "THTHSSSTHSSSTWWWWWWW",
+    "THSHTH",
+    "THSHTHW",
+    "THSHTHWW",
+    "THSHTHWWWWWW",
+    "THSSSTWW",
+    "THSHTHWWWWWWW",
+    "HSHSSSTHSSSWW",
+    "THSHTHT",
+    "STHSTHSSSTHSSSTWWWW",
+    "THSHTHTWWW",
+    "SHTHTHTWW",
+    "HSTHSTHSSSTWWWW",
+    "THSHTHTWWWWW",
+    "THSHTHSSSWW",
+    "THSHTHTWWWWWWW",
+    "STHSSSWW",
+    "SSHSWWW",
+    "THSHTHS",
+    "STHSTHSSSTHSSSTWW",
+    "STHTHSSTHSSSTWWWWWW",
+    "THSHTHSWWWW",
+    "SSSHSSSTWW",
+    "THSHTHSWWWWWW",
+    "THSHTHSWWWWWWW",
+    "STHTHSSTHSSTWWWWWW",
+    "THSHTHST",
+    "STHSSSTWWWWW",
+    "THSHSTHSTWW",
+    "SHTHSTHSSW",
+    "SSSHSTW",
+    "THSHTHSTW",
+    "THSTHSTHTWW",
+    "THSHTHSTWWWWW",
+    "THSHTHSTWWWWWWW",
+    "STHSTHTHSWWWWW",
+    "THSHTHSSWWWW",
+    "THSHTHSSWWWWW",
+    "SSTHSSSTWWWW",
+    "THSHTHSSWWWWWWW",
+    "THSHTHSSTWWW",
+    "THSHTHSSTWWWWWWW",
+    "THSHTHSSS",
+    "THSHTHSSSWWWW",
+    "THTHSSSTWW",
+    "THSHTHSSSWWWWWW",
+    "THSHTHSSSWWWWWWW",
+    "THSHTHSSSTW",
+    "HSHTHSSST",
+    "THSHTHSSSTWWW",
+    "STHTHSSSTHSSSTWW",
+    "THSHTHSSSTWWWWW",
+    "STHTHTHWWWWWW",
+    "THSHSTHWWWWW",
+    "THSTHSTHTWWWWWW",
+    "THSHSTHWWWWWWW",
+    "THSHSTHT",
+    "THSHSTHTW",
+    "THSHSTHTWWW",
+    "STHTWW",
+    "THSHSTHTWWWWWW",
+    "THSHSTHS",
+    "STHTHSTHSSSWWWWWW",
+    "THSHSTHSTW",
+    "HTHSSSTHWW",
+    "THSHSTHSTWWW",
+    "HSTHSTHSSSWWWW",
+    "THSHSTHSSST",
+    "HSTHSTHSSTWW",
+    "HSTHSSSHSS",
+    "THSHSTHSTWWWWW",
+    "THTHSSSHSTWWWWWW",
+    "THSHSTHSSWWW",
+    "HTHSSTHSSWWWWW",
+    "THSHSTHSSWWWW",
+    "THSHSTHSSWWWWW",
+    "THSHSTHSSWWWWWW",
+    "THSHSTHSSWWWWWWW",
+    "THSHSTHSST",
+    "SHSTHSSSTHTWWW",
+    "THSHSTHSSTWWWW",
+    "THSHSTHSSTWWWWWW",
+    "HTHSS",
+    "THSHSTHSSTWWWWWWW",
+    "THSHSTHSSSWW",
+    "THSHSTHSSSWWWWWW",
+    "THSTHSTHSWWWWWWW",
+    "THSHSSSTHSTWWWWWWW",
+    "THSHSTHSSSTW",
+    "THSHSTHSSSTWWWWW",
+    "THTHSTHSSWWWWWWW",
+    "THSHSSTH",
+    "THSTHSTHSSTWWW",
+    "HSTHTHSWWW",
+    "THSHSSTHW",
+    "HTHSTHSSWWWWW",
+    "THSHSSTHWW",
+    "HTHSSSWWWWW",
+    "HTHSSW",
+    "HSHSSSHSSSTWWW",
+    "HSHSSSTHWW",
+    "THSHSSTHWWWW",
+    "HSHSSSHSTWWWWW",
+    "THSHSSTHTWW",
+    "STHSSSTWW",
+    "THSHSSTHTWWWW",
+    "SSTHT",
+    "THSHSSTHSW",
+    "THSHSSTHSWW",
+    "THSHSSTHSWWWW",
+    "HSSSTW",
+    "THSHSSTHSWWWWW",
+    "THSHSSTHSWWWWWW",
+    "SHTHSTHSSTWWWWWW",
+    "SHTWWWW",
+    "THSHSSTHST",
+    "HTHSSTHTW",
+    "HTHSSSTHTWWW",
+    "THSHSSTHSTWWWW",
+    "THSHSSTHSTWWWWWW",
+    "THSHSSTHSTWWWWWWW",
+    "HSTHTHSSST",
+    "THSHSSTHSSW",
+    "THSHSSTHSSWWWWW",
+    "SHSW",
+    "THSHSSTHSSTW",
+    "THTHSTHWW",
+    "TW",
+    "THSHSSTHSSTWW",
+    "THSHSSTHSSTWWW",
+    "STHTHTHWWWWW",
+    "THSHSSTHSSTWWWWW",
+    "THSHSSTHSSTWWWWWW",
+    "THSHSSTHSSTWWWWWWW",
+    "SHSTHSSTHWW",
+    "THSHSSTHSSSWWWWWW",
+    "THSHSSTHSSSTWWWWW",
+    "SHSTHSSSTHSWWWWWWW",
+    "HSTHSSTHSSSWWWWWWW",
+    "THSHTHTWWWWWW",
+    "THSHSSTHSSSTWWWWWWW",
+    "THSHSTHSSW",
+    "THSHSSSTHWWWW",
+    "THSHSSSTHTWW",
+    "STHTHSSTHSSWWWWWWW",
+    "SHSTHSSSTHSSSTWWWWWW",
+    "SHSTHSSTHSST",
+    "SHTHSSTHSSSWWWW",
+    "HSTHSSTHSSSTWWWWWWW",
+    "THSHSSSTHTWWWWWWW",
+    "THSHSSSTHSW",
+    "SHWWWW",
+    "THSHSSSTHSWW",
+    "HSTHSSTHSSSTWW",
+    "THSHSSSTHSWWW",
+    "SSHSSSWWWWWW",
+    "SSTHSTW",
+    "THSHSSSTHSWWWWW",
+    "THSHSSSTHSWWWWWW",
+    "STHSTHSSTHSSTWWWW",
+    "THSHSSSTHSWWWWWWW",
+    "THSTHTHSSSWWWW",
+    "THSHSSSTHSTWW",
+    "THSHSSSTHSTWWWWWW",
+    "HSHSTHTWWWWWW",
+    "THSHSSSTHSSWW",
+    "THSHSSSTHSS",
+    "THTHSSSTHSSTWWW",
+    "THSHSSSTHSSW",
+    "SHSWWWWW",
+    "THSHSSSTHSSWWWWW",
+    "THSHSSSTHSSWWWWWWW",
+    "THSHSSSTHSSTW",
+    "THSTHSSTHSSWWW",
+    "THSHSSSTHSSTWWW",
+    "THTHSSSHTWW",
+    "THSHSSSTHSSTWWWWW",
+    "THSHSSSTHSSTWWWWWW",
+    "THSHSSSTHSSTWWWWWWW"};
+
+// clang-format on
+
+inline domega_matrix_table_t load_s3_table() {
+    using namespace std;
+    domega_matrix_table_t s3_table;
+
+    for (int i = 0; i < S3_TABLE_SIZE; ++i) {
+        auto k = S3_TABLE_KEYS[i];
+        auto v = S3_TABLE_VALUES[i];
+        DOmegaMatrix mat(ZOmega(k[0], k[1], k[2], k[3]),
+                         ZOmega(k[4], k[5], k[6], k[7]), k[8], k[9]);
+        s3_table[mat] = v;
+    }
+    return s3_table;
+}
+
+} // namespace grid_synth
+} // namespace staq
+
+#endif // GRID_SYNTH_S3_TABLE_HPP_
diff --git a/include/synthesis/logic_synthesis.hpp b/include/synthesis/logic_synthesis.hpp
index 00b23a2d..caaa00d4 100644
--- a/include/synthesis/logic_synthesis.hpp
+++ b/include/synthesis/logic_synthesis.hpp
@@ -148,7 +148,7 @@ synthesize_net(parser::Position pos, T& l_net,
     tweedledum::gg_network<tweedledum::mcmt_gate> q_net;
     if (!lutn) {
         std::cerr << "Could not map network into klut network" << std::endl;
-        return std::move(ret);
+        return ret;
     }
 
     // Synthesize a gate graph network with 1, 2, and 3 qubit gates using
@@ -316,7 +316,7 @@ synthesize_net(parser::Position pos, T& l_net,
         }
     });
 
-    return std::move(ret);
+    return ret;
 }
 
 } /* namespace synthesis */
diff --git a/include/transformations/qasm_synth.hpp b/include/transformations/qasm_synth.hpp
index 57dbfc42..62889b6a 100644
--- a/include/transformations/qasm_synth.hpp
+++ b/include/transformations/qasm_synth.hpp
@@ -34,9 +34,9 @@
 
 #include <cstdlib>
 #include <list>
-#include <variant>
 
 #include "grid_synth/exact_synthesis.hpp"
+#include "grid_synth/grid_synth.hpp"
 #include "grid_synth/rz_approximation.hpp"
 #include "grid_synth/types.hpp"
 #include "qasmtools/ast/replacer.hpp"
@@ -46,16 +46,15 @@ namespace staq {
 namespace transformations {
 
 namespace ast = qasmtools::ast;
-using real_t = staq::grid_synth::real_t;
+using namespace grid_synth;
 
 /* Implementation */
-class ReplaceRotationsImpl final : public ast::Replacer {
+class QASMSynthImpl final : public ast::Replacer {
   public:
-    ReplaceRotationsImpl(grid_synth::domega_matrix_table_t& s3_table,
-                         real_t& eps, bool check, bool details, bool verbose)
-        : s3_table_(s3_table), eps_(eps), check_(check), details_(details),
-          verbose_(verbose), w_count_(0){};
-    ~ReplaceRotationsImpl() = default;
+    QASMSynthImpl(const GridSynthOptions& opt)
+        : synthesizer_(make_synthesizer(opt)), w_count_(0), check_(opt.check),
+          details_(opt.details), verbose_(opt.verbose){};
+    ~QASMSynthImpl() = default;
 
     void run(ast::ASTNode& node) { node.accept(*this); }
 
@@ -94,18 +93,19 @@ class ReplaceRotationsImpl final : public ast::Replacer {
                           << ": finding approximation for angle = " << (angle)
                           << '\n';
             }
-            std::string rz_approx = get_rz_approx(angle);
+            std::string op_str = synthesizer_.get_op_str(angle);
             if (details_) {
-                std::cerr << gate.pos() << ": found approximation " << rz_approx
+                std::cerr << gate.pos() << ": found approximation " << op_str
                           << '\n';
             }
 
-            for (char c : rz_approx) {
+            for (char c : op_str) {
                 if (c == 'w' || // If the approximation creates w or W gates,
                     c == 'W') { // collect them and output the global phase
                                 // later.
                     if (gate.qargs()[0].offset() == std::nullopt) {
-                        std::cerr << "Please inline the qasm code first."
+                        std::cerr << "Please inline the qasm code first and "
+                                     "clear declarations."
                                   << std::endl;
                         exit(EXIT_FAILURE);
                     }
@@ -142,7 +142,7 @@ class ReplaceRotationsImpl final : public ast::Replacer {
      * This accounts for all collected w and W gates.
      */
     void print_global_phase() {
-        int a = (w_count_ % 16 + 16) % 16; // Normalize a to the range [0, 16)
+        int a = get_w_count();
         if (a == 0)
             return;
         std::cout << "// global-phase: exp i*pi " << a << " " << 8 << std::endl;
@@ -164,28 +164,18 @@ class ReplaceRotationsImpl final : public ast::Replacer {
 #endif
     }
 
+    // Normalize to the range [0, 16)
+    int get_w_count() const { return (w_count_ % 16 + 16) % 16; }
+
   private:
-    real_t& eps_;
-    grid_synth::domega_matrix_table_t& s3_table_;
+    GridSynthesizer synthesizer_;
+    int w_count_;
     bool check_;
     bool details_;
     bool verbose_;
-    std::unordered_map<std::string, std::string> rz_approx_cache_;
-    int w_count_;
-
-    /**
-     * Converts a GMP float to a string representation suitable for hashing.
-     */
-    std::string to_string(const mpf_class& x) const {
-        mp_exp_t exp;
-        // Use base 32 to get a shorter string.
-        std::string s =
-            x.get_str(exp, 32).substr(0, mpf_get_default_prec() / 5);
-        return s + std::string(" ") + std::to_string(exp);
-    }
 
     /*!
-     * \brief Makes a new gate with no cargs.
+     * \brief Copies a gate; gives it a new name and no cargs.
      *
      * \param name The name of the new gate.
      * \param gate The gate to make a copy of.
@@ -197,100 +187,16 @@ class ReplaceRotationsImpl final : public ast::Replacer {
         return std::make_unique<ast::DeclaredGate>(ast::DeclaredGate(
             gate.pos(), name, std::move(c_args), std::move(q_args)));
     }
-
-    /*! \brief Find RZ-approximation for an angle using grid_synth. */
-    std::string get_rz_approx(const real_t& angle) {
-        using namespace grid_synth;
-
-        if (verbose_)
-            std::cerr << "Checking common cases..."
-                      << "\n";
-        std::string ret = check_common_cases(angle / gmpf::gmp_pi(), eps_);
-        if (ret != "") {
-            if (details_)
-                std::cerr
-                    << "Angle is multiple of pi/4, answer is known exactly"
-                    << '\n';
-            if (check_)
-                std::cerr << "Check flag = " << 1 << '\n';
-            std::string ret_no_spaces;
-            for (char c : ret) {
-                if (c != ' ')
-                    ret_no_spaces.push_back(c);
-            }
-            return ret_no_spaces;
-        }
-
-        std::string angle_str = to_string(angle);
-        if (verbose_) {
-            std::cerr << "Checking local cache..." << '\n';
-            std::cerr << "Angle has string representation " << angle_str
-                      << '\n';
-        }
-        if (rz_approx_cache_.count(angle_str)) {
-            if (verbose_ || details_)
-                std::cerr << "Angle is found in local cache" << '\n';
-            return rz_approx_cache_[angle_str];
-        }
-
-        if (verbose_)
-            std::cerr << "Running grid_synth to find new rz approximation..."
-                      << '\n';
-        RzApproximation rz_approx =
-            find_fast_rz_approximation(angle / real_t("-2.0"), eps_);
-        if (!rz_approx.solution_found()) {
-            std::cerr << "No approximation found for RzApproximation. "
-                         "Try changing factorization effort."
-                      << '\n';
-            exit(EXIT_FAILURE); // TODO: change this to fail more gracefully?
-        }
-        if (verbose_)
-            std::cerr << "Approximation found. Synthesizing..." << '\n';
-        ret = synthesize(rz_approx.matrix(), s3_table_);
-
-        if (verbose_)
-            std::cerr << "Synthesis complete." << '\n';
-        if (check_) {
-            std::cerr << "Check flag = "
-                      << (rz_approx.matrix() ==
-                          domega_matrix_from_str(full_simplify_str(ret)))
-                      << '\n';
-        }
-        if (details_) {
-            real_t scale = gmpf::pow(SQRT2, rz_approx.matrix().k());
-            std::cerr << "angle = " << std::scientific << angle << '\n';
-            std::cerr << rz_approx.matrix();
-            std::cerr << "u decimal value = "
-                      << "(" << rz_approx.matrix().u().decimal().real() / scale
-                      << "," << rz_approx.matrix().u().decimal().imag() / scale
-                      << ")" << '\n';
-            std::cerr << "t decimal value = "
-                      << "(" << rz_approx.matrix().t().decimal().real() / scale
-                      << "," << rz_approx.matrix().t().decimal().imag() / scale
-                      << ")" << '\n';
-            std::cerr << "error = " << rz_approx.error() << '\n';
-            str_t simplified = full_simplify_str(ret);
-            std::string::difference_type n =
-                count(simplified.begin(), simplified.end(), 'T');
-            std::cerr << "T count = " << n << '\n';
-            std::cerr << "----" << '\n' << std::fixed;
-        }
-
-        rz_approx_cache_[angle_str] = ret;
-        return ret;
-    }
 };
 
 /**
  * Replaces all rx/ry/rz gates in a program with grid_synth approximations.
  */
-void replace_rotations(ast::ASTNode& node,
-                       grid_synth::domega_matrix_table_t& s3_table, real_t& eps,
-                       bool check = false, bool details = false,
-                       bool verbose = false) {
-    ReplaceRotationsImpl alg(s3_table, eps, check, details, verbose);
+int qasm_synth(ast::ASTNode& node, const GridSynthOptions& opt) {
+    QASMSynthImpl alg(opt);
     alg.run(node);
     alg.print_global_phase();
+    return alg.get_w_count();
 }
 
 } /* namespace transformations */
diff --git a/pystaq/staq_wrapper.cpp b/pystaq/staq_wrapper.cpp
index b42b6e52..c518c92b 100644
--- a/pystaq/staq_wrapper.cpp
+++ b/pystaq/staq_wrapper.cpp
@@ -29,6 +29,7 @@
 #endif
 
 #include <pybind11/pybind11.h>
+#include <pybind11/stl.h>
 #include <sstream>
 
 #include "qasmtools/parser/parser.hpp"
@@ -39,6 +40,12 @@
 #include "transformations/inline.hpp"
 #include "transformations/oracle_synthesizer.hpp"
 
+#ifdef GRID_SYNTH
+#include "grid_synth/grid_synth.hpp"
+#include "grid_synth/types.hpp"
+#include "transformations/qasm_synth.hpp"
+#endif
+
 #include "optimization/cnot_resynthesis.hpp"
 #include "optimization/rotation_folding.hpp"
 #include "optimization/simplify.hpp"
@@ -139,6 +146,14 @@ class Program {
     void synthesize_oracles() {
         staq::transformations::synthesize_oracles(*prog_);
     }
+#ifdef GRID_SYNTH
+    void qasm_synth(long int prec, int factor_effort, bool check, bool details,
+                    bool verbose) {
+        staq::grid_synth::GridSynthOptions opt{prec, factor_effort, check,
+                                               details, verbose};
+        staq::transformations::qasm_synth(*prog_, opt);
+    }
+#endif /* GRID_SYNTH */
     // output (these methods return a string)
     std::string get_resources(bool box_gates = false, bool unbox_qelib = false,
                               bool no_merge_dagger = false) {
@@ -206,7 +221,34 @@ void rotation_fold(Program& prog, bool no_correction) {
 void cnot_resynth(Program& prog) { prog.cnot_resynth(); }
 void simplify(Program& prog, bool no_fixpoint) { prog.simplify(no_fixpoint); }
 void synthesize_oracles(Program& prog) { prog.synthesize_oracles(); }
-
+#ifdef GRID_SYNTH
+void grid_synth(const std::vector<std::string>& thetas, long int prec,
+                int factor_effort, bool check, bool details, bool verbose,
+                bool timer) {
+    using namespace staq::grid_synth;
+    if (verbose)
+        std::cerr << thetas.size() << " angle(s) read." << '\n';
+    GridSynthOptions opt{prec, factor_effort, check, details, verbose, timer};
+    GridSynthesizer synthesizer = make_synthesizer(opt);
+    std::random_device rd;
+    random_numbers.seed(rd());
+    for (const auto& angle : thetas) {
+        str_t op_str = synthesizer.get_op_str(real_t(angle));
+        for (char c : op_str)
+            std::cout << c << ' ';
+        std::cout << '\n';
+    }
+}
+void grid_synth(const std::string& theta, long int prec, int factor_effort,
+                bool check, bool details, bool verbose, bool timer) {
+    grid_synth(std::vector<std::string>{theta}, prec, factor_effort, check,
+               details, verbose, timer);
+}
+void qasm_synth(Program& prog, long int prec, int factor_effort, bool check,
+                bool details, bool verbose) {
+    prog.qasm_synth(prec, factor_effort, check, details, verbose);
+}
+#endif /* GRID_SYNTH */
 std::string lattice_surgery(Program& prog) { return prog.lattice_surgery(); }
 
 static double FIDELITY_1 = staq::mapping::FIDELITY_1;
@@ -294,6 +336,30 @@ PYBIND11_MODULE(pystaq, m) {
           py::arg("prog"), py::arg("no_fixpoint") = false);
     m.def("synthesize_oracles", &synthesize_oracles,
           "Synthesizes oracles declared by verilog files");
+#ifdef GRID_SYNTH
+    m.def("grid_synth",
+          py::overload_cast<const std::vector<std::string>&, long int, int,
+                            bool, bool, bool, bool>(&grid_synth),
+          "Approximate Z-rotation angle(s) (in units of PI)", py::arg("theta"),
+          py::arg("prec"),
+          py::arg("pollard-rho") = staq::grid_synth::MAX_ATTEMPTS_POLLARD_RHO,
+          py::arg("check") = false, py::arg("details") = false,
+          py::arg("verbose") = false, py::arg("timer") = false);
+    m.def("grid_synth",
+          py::overload_cast<const std::string&, long int, int,
+                            bool, bool, bool, bool>(&grid_synth),
+          "Approximate Z-rotation angle(s) (in units of PI)", py::arg("theta"),
+          py::arg("prec"),
+          py::arg("pollard-rho") = staq::grid_synth::MAX_ATTEMPTS_POLLARD_RHO,
+          py::arg("check") = false, py::arg("details") = false,
+          py::arg("verbose") = false, py::arg("timer") = false);
+    m.def("qasm_synth", &qasm_synth,
+          "Replaces rx/ry/rz gates with grid_synth approximations",
+          py::arg("prog"), py::arg("prec"),
+          py::arg("pollard-rho") = staq::grid_synth::MAX_ATTEMPTS_POLLARD_RHO,
+          py::arg("check") = false, py::arg("details") = false,
+          py::arg("verbose") = false);
+#endif /* GRID_SYNTH */
     m.def("lattice_surgery", &lattice_surgery,
           "Compiles OpenQASM2 to lattice surgery instruction set",
           py::arg("prog"));
diff --git a/setup.py b/setup.py
index 5884780e..ea30dee4 100644
--- a/setup.py
+++ b/setup.py
@@ -3,7 +3,42 @@
 from pybind11.setup_helpers import Pybind11Extension
 from setuptools import setup
 
+import ctypes as ct  # to call native
+import ctypes.util as ctu
+import platform  # to learn the OS we're on
+
 extra_compile_args = ["-Ilibs", "-Iinclude", "-Iqasmtools/include"]
+extra_links_args = []
+
+
+def _load_shared_obj(name):
+    """Attempts to load native OQS library."""
+    paths = []
+
+    # search typical locations
+    paths += [ctu.find_library(name)]
+    paths += [ctu.find_library("lib" + name)]
+    dll = ct.windll if platform.system() == "Windows" else ct.cdll
+
+    for path in paths:
+        if path:
+            lib = dll.LoadLibrary(path)
+            return lib
+
+    raise RuntimeError("No " + name + " shared libraries found")
+
+
+found_GMP = True
+try:
+    _libgmp = _load_shared_obj("gmp")
+    _libgmpxx = _load_shared_obj("gmpxx")
+except:
+    found_GMP = False
+
+if found_GMP:
+    extra_compile_args.append("-DGRID_SYNTH")
+    extra_compile_args.append("-DEXPR_GMP")
+    extra_links_args = ["-lgmp", "-lgmpxx"]
 
 # If the platform seem to be MSVC
 if sys.platform == "win32" and not sys.platform == "cygwin" and not sys.platform == "msys":
@@ -14,6 +49,7 @@
         "pystaq",
         ["pystaq/staq_wrapper.cpp"],
         extra_compile_args=extra_compile_args,
+        extra_link_args=extra_links_args,
         cxx_std=17,
         include_pybind11=False,
     ),
diff --git a/tools/CMakeLists.txt b/tools/CMakeLists.txt
index 5d9f6a97..ac93642f 100644
--- a/tools/CMakeLists.txt
+++ b/tools/CMakeLists.txt
@@ -2,16 +2,22 @@ file(GLOB FILENAMES *.cpp)
 
 add_custom_target(tools COMMENT "Build all binary tools.")
 
-if (${BUILD_GRID_SYNTH})
-    if (MSVC)
-        # gmp, gmpxx
-        find_package(PkgConfig REQUIRED)
+set(BUILD_GRID_SYNTH OFF)
+if (MSVC)
+    # gmp, gmpxx
+    find_package(PkgConfig REQUIRED)
+    if (PkgConfig_FOUND)
         pkg_check_modules(gmp REQUIRED IMPORTED_TARGET gmp)
         pkg_check_modules(gmpxx REQUIRED IMPORTED_TARGET gmpxx)
-    else ()
-        find_package(GMP REQUIRED)
+        set(BUILD_GRID_SYNTH ON)
+        add_compile_options("-DEXPR_GMP")
+    endif ()
+else ()
+    find_package(GMP REQUIRED)
+    if (GMP_FOUND)
+        set(BUILD_GRID_SYNTH ON)
+        add_compile_options("-DEXPR_GMP")
     endif ()
-    add_compile_options("-DEXPR_GMP")
 endif ()
 
 foreach (filename ${FILENAMES})
diff --git a/tools/grid_synth.cpp b/tools/grid_synth.cpp
index b7718f6c..01fd4c2c 100644
--- a/tools/grid_synth.cpp
+++ b/tools/grid_synth.cpp
@@ -31,45 +31,36 @@
 #include <vector>
 
 #include "grid_synth/exact_synthesis.hpp"
+#include "grid_synth/grid_synth.hpp"
 #include "grid_synth/regions.hpp"
 #include "grid_synth/rz_approximation.hpp"
 #include "grid_synth/types.hpp"
 
 int main(int argc, char** argv) {
-
     using namespace staq;
     using namespace grid_synth;
 
     bool check = false, details = false, verbose = false, timer = false;
-    real_t theta, eps;
     std::vector<std::string> thetas;
-    std::vector<long int> prec_lst;
     long int prec;
     int factor_effort;
-    domega_matrix_table_t s3_table;
-    str_t tablefile{};
 
     CLI::App app{"Grid Synthesis"};
 
     CLI::Option* thetas_op =
-        app.add_option("-t, --theta", thetas,
-                       "Z-rotation angle(s) in units of PI")
-            ->required();
+        app.add_option("theta", thetas,
+                       "Z-rotation angle(s) in units of PI");
     CLI::Option* prec_opt =
         app.add_option<long int, int>(
                "-p, --precision", prec,
                "Precision in base ten as a positive integer (10^-p)")
             ->required();
-    CLI::Option* fact_eff = app.add_option<int, int>(
-        "--pollard-rho", factor_effort,
-        "Sets MAX_ATTEMPTS_POLLARD_RHO, the effort "
-        "taken to factorize candidate solutions (default=200)");
-    CLI::Option* read = app.add_option("-r, --read-table", tablefile,
-                                       "Name of file containing s3_table");
-    CLI::Option* write =
-        app.add_option("-w, --write-table", tablefile,
-                       "Name of table file to write s3_table to")
-            ->excludes(read);
+    CLI::Option* fact_eff =
+        app.add_option<int, int>(
+               "--pollard-rho", factor_effort,
+               "Sets MAX_ATTEMPTS_POLLARD_RHO, the effort "
+               "taken to factorize candidate solutions (default=200)")
+            ->default_val(MAX_ATTEMPTS_POLLARD_RHO);
     app.add_flag("-c, --check", check,
                  "Output bool that will be 1 if the op string matches the "
                  "input operator");
@@ -84,170 +75,32 @@ int main(int argc, char** argv) {
 
     CLI11_PARSE(app, argc, argv);
 
-    if (verbose) {
-        std::cerr << thetas.size() << " angles read." << '\n';
-    }
-
-    if (*read) {
-        if (verbose) {
-            std::cerr << "Reading s3_table from " << tablefile << '\n';
-        }
-        s3_table = read_s3_table(tablefile);
-    } else if (*write) {
-        if (verbose) {
-            std::cerr << "Generating new table file and writing to "
-                      << tablefile << '\n';
-        }
-        s3_table = generate_s3_table();
-        write_s3_table(tablefile, s3_table);
-    } else if (std::ifstream(DEFAULT_TABLE_FILE)) {
-        if (verbose) {
-            std::cerr << "Table file found at default location "
-                      << DEFAULT_TABLE_FILE << '\n';
-        }
-        s3_table = read_s3_table(DEFAULT_TABLE_FILE);
-    } else {
-        if (verbose) {
-            std::cerr << "Failed to find " << DEFAULT_TABLE_FILE
-                      << ". Generating new table file and writing to "
-                      << DEFAULT_TABLE_FILE << '\n';
-        }
-        s3_table = generate_s3_table();
-        write_s3_table(DEFAULT_TABLE_FILE, s3_table);
-    }
+    if (verbose)
+        std::cerr << thetas.size() << " angle(s) read." << '\n';
 
-    MP_CONSTS = initialize_constants(prec);
-    eps = gmpf::pow(real_t(10), -prec);
+    GridSynthOptions opt{prec, factor_effort, check, details, verbose, timer};
+    GridSynthesizer synthesizer = make_synthesizer(opt);
 
-    if (*fact_eff) {
-        MAX_ATTEMPTS_POLLARD_RHO = factor_effort;
-    }
-
-    if (verbose) {
-        std::cerr << "Runtime Parameters" << '\n';
-        std::cerr << "------------------" << '\n';
-        std::cerr << std::setw(3 * COLW) << std::left
-                  << "TOL (Tolerance for float equality) " << std::setw(1)
-                  << ": " << std::setw(3 * COLW) << std::left << std::scientific
-                  << TOL << '\n';
-        std::cerr << std::setw(3 * COLW) << std::left
-                  << "KMIN (Minimum scaling exponent) " << std::setw(1) << ": "
-                  << std::setw(3 * COLW) << std::left << std::fixed << KMIN
-                  << '\n';
-        std::cerr << std::setw(2 * COLW) << std::left
-                  << "KMAX (Maximum scaling exponent) " << std::setw(1) << ": "
-                  << std::setw(3 * COLW) << std::left << std::fixed << KMAX
-                  << '\n';
-        std::cerr << std::setw(3 * COLW) << std::left
-                  << "MAX_ATTEMPTS_POLLARD_RHO (How hard we try to factor) "
-                  << std::setw(1) << ": " << std::setw(3 * COLW) << std::left
-                  << MAX_ATTEMPTS_POLLARD_RHO << '\n';
-        std::cerr << std::setw(3 * COLW) << std::left
-                  << "MAX_ITERATIONS_FERMAT_TEST (How hard we try to check "
-                     "primality) "
-                  << std::setw(1) << ": " << std::setw(3 * COLW) << std::left
-                  << MAX_ITERATIONS_FERMAT_TEST << '\n';
-    }
-    std::cerr << std::scientific;
-
-    long long duration = 0;
     if (*prec_opt && *thetas_op) {
         std::random_device rd;
         random_numbers.seed(rd());
 
         for (const auto& angle : thetas) {
-            str_t common_case = check_common_cases(real_t(angle), eps);
-            if (verbose)
-                std::cerr << "Checking common cases..." << '\n';
-            if (common_case != "") {
-                if (details)
-                    std::cerr
-                        << "Angle is multiple of pi/4, answer is known exactly"
-                        << '\n';
-                if (check) {
-                    std::cerr << "Check flag = " << 1 << '\n';
-                }
-                std::cout << common_case << '\n';
-                return 0;
-            }
-            if (verbose)
-                std::cerr << "No common cases found" << '\n';
-
-            RzApproximation rz_approx;
-            if (timer) {
-                auto start = std::chrono::steady_clock::now();
-                rz_approx = find_fast_rz_approximation(
-                    real_t(angle) * PI / real_t("-2"), eps);
-                str_t op_str = synthesize(rz_approx.matrix(), s3_table);
-                auto end = std::chrono::steady_clock::now();
-                duration +=
-                    std::chrono::duration_cast<std::chrono::microseconds>(end -
-                                                                          start)
-                        .count();
-            } else {
-                if (verbose) {
-                    std::cerr << "----\n";
-                    std::cerr << "Finding approximation for angle = " << (angle)
-                              << "..." << '\n';
-                }
-                rz_approx = find_fast_rz_approximation(
-                    real_t(angle) * PI / real_t("-2"), eps);
-                if (!rz_approx.solution_found()) {
-                    std::cerr << "No approximation found for RzApproximation. "
-                                 "Try changing factorization effort."
-                              << '\n';
-                    return EXIT_FAILURE;
-                }
-                if (verbose) {
-                    std::cerr << "Approximation found. Synthesizing..." << '\n';
-                }
-                str_t op_str = synthesize(rz_approx.matrix(), s3_table);
-                if (verbose) {
-                    std::cerr << "Synthesis complete." << '\n';
-                }
-
-                if (check) {
-                    std::cerr
-                        << "Check flag = "
-                        << (rz_approx.matrix() ==
-                            domega_matrix_from_str(full_simplify_str(op_str)))
-                        << '\n';
-                }
-
-                if (details) {
-                    real_t scale = gmpf::pow(SQRT2, rz_approx.matrix().k());
-                    std::cerr << "angle = " << angle << '\n';
-                    std::cerr << rz_approx.matrix();
-                    std::cerr << "u decimal value = "
-                              << "("
-                              << rz_approx.matrix().u().decimal().real() / scale
-                              << ","
-                              << rz_approx.matrix().u().decimal().imag() / scale
-                              << ")" << '\n';
-                    std::cerr << "t decimal value = "
-                              << "("
-                              << rz_approx.matrix().t().decimal().real() / scale
-                              << ","
-                              << rz_approx.matrix().t().decimal().imag() / scale
-                              << ")" << '\n';
-                    std::cerr << "error = " << rz_approx.error() << '\n';
-                    str_t simplified = full_simplify_str(op_str);
-                    std::string::difference_type n =
-                        count(simplified.begin(), simplified.end(), 'T');
-                    std::cerr << "T count = " << n << '\n';
-                    std::cerr << "----" << '\n';
-                }
-
-                for (auto& ch : full_simplify_str(op_str)) {
-                    std::cout << ch << " ";
-                }
-                std::cout << '\n';
-            }
+            str_t op_str =
+                synthesizer.get_op_str(real_t(angle) * gmpf::gmp_pi());
+            for (char c : op_str)
+                std::cout << c << ' ';
+            std::cout << '\n';
         }
     }
 
     if (timer) {
-        std::cerr << "Duration = " << (static_cast<double>(duration) / 1e6)
-                  << '\n';
+        std::cerr << std::fixed
+                    << "Duration = " << synthesizer.get_duration()
+                    << " seconds" << '\n';
+    } 
+    else {
+        std::cerr << "No angle provided. Exiting.\n";
+        return 0;
     }
 }
diff --git a/tools/qasm_synth.cpp b/tools/qasm_synth.cpp
index 732fc852..b755f22a 100644
--- a/tools/qasm_synth.cpp
+++ b/tools/qasm_synth.cpp
@@ -38,31 +38,23 @@ int main(int argc, char** argv) {
     using qasmtools::parser::parse_stdin;
 
     bool check = false, details = false, verbose = false;
-    real_t eps;
     long int prec;
     int factor_effort;
     domega_matrix_table_t s3_table;
-    str_t tablefile{};
 
     CLI::App app{"Grid Synthesis rx/ry/rz substitution"};
 
-    // this interface is more or less identical to that of grid_synth.cpp
-    // TODO: consider factoring out duplicated code?
     CLI::Option* prec_opt =
         app.add_option<long int, int>(
                "-p, --precision", prec,
                "Precision in base ten as a positive integer (10^-p)")
             ->required();
-    CLI::Option* fact_eff = app.add_option<int, int>(
-        "--pollard-rho", factor_effort,
-        "Sets MAX_ATTEMPTS_POLLARD_RHO, the effort "
-        "taken to factorize candidate solutions (default=200)");
-    CLI::Option* read = app.add_option("-r, --read-table", tablefile,
-                                       "Name of file containing s3_table");
-    CLI::Option* write =
-        app.add_option("-w, --write-table", tablefile,
-                       "Name of table file to write s3_table to")
-            ->excludes(read);
+    CLI::Option* fact_eff =
+        app.add_option<int, int>(
+               "--pollard-rho", factor_effort,
+               "Sets MAX_ATTEMPTS_POLLARD_RHO, the effort "
+               "taken to factorize candidate solutions (default=200)")
+            ->default_val(MAX_ATTEMPTS_POLLARD_RHO);
     app.add_flag("-c, --check", check,
                  "Output bool that will be 1 if the op string matches the "
                  "input operator");
@@ -76,75 +68,16 @@ int main(int argc, char** argv) {
 
     CLI11_PARSE(app, argc, argv);
 
-    if (*read) {
-        if (verbose) {
-            std::cerr << "Reading s3_table from " << tablefile << '\n';
-        }
-        s3_table = read_s3_table(tablefile);
-    } else if (*write) {
-        if (verbose) {
-            std::cerr << "Generating new table file and writing to "
-                      << tablefile << '\n';
-        }
-        s3_table = generate_s3_table();
-        write_s3_table(tablefile, s3_table);
-    } else if (std::ifstream(DEFAULT_TABLE_FILE)) {
-        if (verbose) {
-            std::cerr << "Table file found at default location "
-                      << DEFAULT_TABLE_FILE << '\n';
-        }
-        s3_table = read_s3_table(DEFAULT_TABLE_FILE);
-    } else {
-        if (verbose) {
-            std::cerr << "Failed to find " << DEFAULT_TABLE_FILE
-                      << ". Generating new table file and writing to "
-                      << DEFAULT_TABLE_FILE << '\n';
-        }
-        s3_table = generate_s3_table();
-        write_s3_table(DEFAULT_TABLE_FILE, s3_table);
-    }
-
-    MP_CONSTS = initialize_constants(prec);
-    eps = gmpf::pow(real_t(10), -prec);
-
-    if (*fact_eff) {
-        MAX_ATTEMPTS_POLLARD_RHO = factor_effort;
-    }
-
-    if (verbose) {
-        std::cerr << "Runtime Parameters" << '\n';
-        std::cerr << "------------------" << '\n';
-        std::cerr << std::setw(3 * COLW) << std::left
-                  << "TOL (Tolerance for float equality) " << std::setw(1)
-                  << ": " << std::setw(3 * COLW) << std::left << std::scientific
-                  << TOL << '\n';
-        std::cerr << std::setw(3 * COLW) << std::left
-                  << "KMIN (Minimum scaling exponent) " << std::setw(1) << ": "
-                  << std::setw(3 * COLW) << std::left << std::fixed << KMIN
-                  << '\n';
-        std::cerr << std::setw(2 * COLW) << std::left
-                  << "KMAX (Maximum scaling exponent) " << std::setw(1) << ": "
-                  << std::setw(3 * COLW) << std::left << std::fixed << KMAX
-                  << '\n';
-        std::cerr << std::setw(3 * COLW) << std::left
-                  << "MAX_ATTEMPTS_POLLARD_RHO (How hard we try to factor) "
-                  << std::setw(1) << ": " << std::setw(3 * COLW) << std::left
-                  << MAX_ATTEMPTS_POLLARD_RHO << '\n';
-        std::cerr << std::setw(3 * COLW) << std::left
-                  << "MAX_ITERATIONS_FERMAT_TEST (How hard we try to check "
-                     "primality) "
-                  << std::setw(1) << ": " << std::setw(3 * COLW) << std::left
-                  << MAX_ITERATIONS_FERMAT_TEST << '\n';
-    }
-    std::cerr << std::scientific;
+    GridSynthOptions opt{prec, factor_effort, check, details, verbose};
 
-    auto program = parse_stdin("", true); // parse stdin using GMP
+    // Must initialize constants before parsing stdin using GMP
+    MP_CONSTS = initialize_constants(opt.prec);
+    auto program = parse_stdin("", true);
     if (program) {
-        transformations::replace_rotations(*program, s3_table, eps, check,
-                                           details, verbose);
+        transformations::qasm_synth(*program, opt);
         std::cout << *program;
     } else {
         std::cerr << "Parsing failed\n";
-        return 1;
+        return EXIT_FAILURE;
     }
 }
diff --git a/unit_tests/CMakeLists.txt b/unit_tests/CMakeLists.txt
index f2a6014b..5c7d91bf 100644
--- a/unit_tests/CMakeLists.txt
+++ b/unit_tests/CMakeLists.txt
@@ -9,14 +9,21 @@ if (MSVC)
     endif ()
 endif ()
 
-if (${BUILD_GRID_SYNTH})
-    if (MSVC)
-        # gmp, gmpxx
-        find_package(PkgConfig REQUIRED)
+set(BUILD_GRID_SYNTH OFF)
+if (MSVC)
+    # gmp, gmpxx
+    find_package(PkgConfig REQUIRED)
+    if (PkgConfig_FOUND)
         pkg_check_modules(gmp REQUIRED IMPORTED_TARGET gmp)
         pkg_check_modules(gmpxx REQUIRED IMPORTED_TARGET gmpxx)
-    else ()
-        find_package(GMP REQUIRED)
+        set(BUILD_GRID_SYNTH ON)
+        add_compile_options("-DEXPR_GMP")
+    endif ()
+else ()
+    find_package(GMP REQUIRED)
+    if (GMP_FOUND)
+        set(BUILD_GRID_SYNTH ON)
+        add_compile_options("-DEXPR_GMP")
     endif ()
 endif ()
 
diff --git a/unit_tests/tests/grid_synth/grid_synth.cpp b/unit_tests/tests/grid_synth/grid_synth.cpp
new file mode 100644
index 00000000..6655096a
--- /dev/null
+++ b/unit_tests/tests/grid_synth/grid_synth.cpp
@@ -0,0 +1,38 @@
+#include "grid_synth/grid_synth.hpp"
+#include "gtest/gtest.h"
+
+using namespace staq;
+using namespace grid_synth;
+
+// Synthesize multiples of pi/4
+TEST(GridSynth, ExactSynthesis) {
+    GridSynthOptions opt{100, 200, false, false, false, false};
+    GridSynthesizer synthesizer = make_synthesizer(opt);
+
+    for (int i = -20; i <= 20; ++i) {
+        real_t angle = real_t(i) / real_t(4);
+        str_t op_str = synthesizer.get_op_str(angle * gmpf::gmp_pi());
+        real_t eps = gmpf::pow(real_t(10), -100);
+        str_t common_case = check_common_cases(angle, eps);
+        EXPECT_TRUE(op_str == common_case);
+    }
+}
+
+// Synthesize other angles
+TEST(GridSynth, InexactSynthesis) {
+    GridSynthOptions opt{100, 200, false, false, false, false};
+    GridSynthesizer synthesizer = make_synthesizer(opt);
+    EXPECT_TRUE(synthesizer.is_valid());
+
+    synthesizer.get_op_str(real_t("0.3"));
+    EXPECT_TRUE(synthesizer.is_valid());
+
+    synthesizer.get_op_str(real_t("0.3"));
+    EXPECT_TRUE(synthesizer.is_valid());
+
+    synthesizer.get_op_str(real_t("5.3423"));
+    EXPECT_TRUE(synthesizer.is_valid());
+
+    synthesizer.get_op_str(real_t("-5.3123"));
+    EXPECT_TRUE(synthesizer.is_valid());
+}
diff --git a/unit_tests/tests/grid_synth/qasm_synth.cpp b/unit_tests/tests/grid_synth/qasm_synth.cpp
new file mode 100644
index 00000000..68ac01c3
--- /dev/null
+++ b/unit_tests/tests/grid_synth/qasm_synth.cpp
@@ -0,0 +1,154 @@
+#include "gtest/gtest.h"
+
+#include "qasmtools/parser/parser.hpp"
+#include "transformations/qasm_synth.hpp"
+
+using namespace staq;
+using namespace grid_synth;
+using qasmtools::parser::parse_string;
+
+// Tests rz gate replacement.
+// A multiple of pi/4 is used so that the result is deterministic.
+TEST(QasmSynth, ExactSynthesis) {
+    std::string pre = "OPENQASM 2.0;\n"
+                      "include \"qelib1.inc\";\n"
+                      "\n"
+                      "qreg q[2];\n"
+                      "rz(2*pi/4) q[0];\n";
+
+    std::string post = "OPENQASM 2.0;\n"
+                       "include \"qelib1.inc\";\n"
+                       "\n"
+                       "qreg q[2];\n"
+                       "s q[0];\n";
+
+    auto program = parse_string(pre, "exact_synthesis.qasm");
+    GridSynthOptions opt{100, 200, false, false, false, false};
+    int w_count = transformations::qasm_synth(*program, opt);
+    EXPECT_EQ(w_count, 14);
+
+    std::stringstream ss;
+    ss << *program;
+    EXPECT_EQ(ss.str(), post);
+}
+
+// Tests collection of w and W gates into the global phase.
+TEST(QasmSynth, GlobalPhase) {
+    std::string pre = "OPENQASM 2.0;\n"
+                      "include \"qelib1.inc\";\n"
+                      "\n"
+                      "qreg q[2];\n"
+                      "rz(pi/2) q[0];\n"  // phase += 14/8
+                      "rz(pi/4) q[0];\n"; // phase -= 1/8
+
+    // 32 of these gates should not modify the global phase
+    for (int i = 0; i < 32; ++i) {
+        pre += "rz(pi/2) q[0];\n";
+    }
+
+    auto program = parse_string(pre, "global_phase.qasm");
+    GridSynthOptions opt{100, 200, false, false, false, false};
+    int w_count = transformations::qasm_synth(*program, opt);
+    EXPECT_EQ(w_count, 13); // phase should be 13/8
+}
+
+// Tests rz gate replacement when the exact solution is not known.
+// Also tests GMP expression parsing, and angle caching in GridSynthesizer.
+TEST(QasmSynth, InexactSynthesis) {
+    std::string pre = "OPENQASM 2.0;\n"
+                      "include \"qelib1.inc\";\n"
+                      "\n"
+                      "qreg q[2];\n"
+                      "rz(-0.3) q[0];\n"  // These three rz gates all
+                      "rz(-3/10) q[0];\n" //  have the same angle
+                      "rz(9*-27/100*10/81) q[0];\n";
+
+    auto program = parse_string(pre, "inexact_synthesis.qasm");
+    GridSynthOptions opt{5, 200, false, false, false, false};
+    transformations::qasm_synth(*program, opt);
+    std::stringstream ss;
+    ss << *program;
+
+    // Grab the rz gate replacements.
+    std::vector<std::string> gates;
+    std::string line;
+    bool push = false;
+    while (getline(ss, line)) {
+        if (push) {
+            gates.push_back(line);
+        } else if (line == "qreg q[2];") {
+            push = true;
+        }
+    }
+
+    // Although rz inexact synthesis is non-deterministic, these rz gates have
+    //  the same angle, and thus they should have the same replacement due to
+    //  GridSynthesizer angle caching.
+    int N = gates.size();
+    EXPECT_TRUE(N > 1);
+    EXPECT_TRUE(N % 3 == 0);
+    for (int i = 0; i < gates.size() / 3; ++i) {
+        EXPECT_EQ(gates[i], gates[i + N / 3]);
+        EXPECT_EQ(gates[i], gates[i + 2 * N / 3]);
+    }
+}
+
+// Tests rx gate replacement.
+// A multiple of pi/4 is used so that the result is deterministic.
+TEST(QasmSynth, rx) {
+    std::string pre = "OPENQASM 2.0;\n"
+                      "include \"qelib1.inc\";\n"
+                      "\n"
+                      "qreg q[2];\n"
+                      "rx(pi) q[1];\n";
+
+    std::string post = "OPENQASM 2.0;\n"
+                       "include \"qelib1.inc\";\n"
+                       "\n"
+                       "qreg q[2];\n"
+                       "h q[1];\n"
+                       "s q[1];\n"
+                       "s q[1];\n"
+                       "h q[1];\n";
+
+    auto program = parse_string(pre, "exact_synthesis.qasm");
+    GridSynthOptions opt{100, 200, false, false, false, false};
+    int w_count = transformations::qasm_synth(*program, opt);
+    EXPECT_EQ(w_count, 12);
+
+    std::stringstream ss;
+    ss << *program;
+    EXPECT_EQ(ss.str(), post);
+}
+
+// Tests ry gate replacement.
+// A multiple of pi/4 is used so that the result is deterministic.
+// Also tests logic for handling common cases in the range [2,4).
+TEST(QasmSynth, ry) {
+    std::string pre = "OPENQASM 2.0;\n"
+                      "include \"qelib1.inc\";\n"
+                      "\n"
+                      "qreg q[2];\n"
+                      "ry(15/2*pi) q[1];\n";
+
+    std::string post = "OPENQASM 2.0;\n"
+                       "include \"qelib1.inc\";\n"
+                       "\n"
+                       "qreg q[2];\n"
+                       "s q[1];\n"
+                       "h q[1];\n"
+                       "s q[1];\n"
+                       "s q[1];\n"
+                       "s q[1];\n"
+                       "h q[1];\n"
+                       "sdg q[1];\n";
+
+    auto program = parse_string(pre, "exact_synthesis.qasm");
+    GridSynthOptions opt{100, 200, false, false, false, false};
+    int w_count = transformations::qasm_synth(*program, opt);
+    EXPECT_EQ(w_count, 2);
+
+    std::stringstream ss;
+    ss << *program;
+    EXPECT_EQ(ss.str(), post);
+}