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\n#include \n#include \n\n// Fast modular multiplication by barrett reduction\n// Reference: https://en.wikipedia.org/wiki/Barrett_reduction\n// NOTE: reconsider after Ice Lake\nstruct barrett {\n unsigned int _m;\n unsigned long long im;\n\n // @param m `1 <= m < 2^31`\n explicit barrett(unsigned int m)\n : _m(m), im((unsigned long long)(-1) / m + 1) {}\n\n // @return m\n unsigned int umod() const { return _m; }\n\n // @param a `0 <= a < m`\n // @param b `0 <= b < m`\n // @return `a * b % m`\n unsigned int mul(unsigned int a, unsigned int b) const {\n // [1] m = 1\n // a = b = im = 0, so okay\n\n // [2] m >= 2\n // im = ceil(2^64 / m)\n // -> im * m = 2^64 + r (0 <= r < m)\n // let z = a*b = c*m + d (0 <= c, d < m)\n // a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im\n // c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1)\n // < 2^64 * 2\n // ((ab * im) >> 64) == c or c + 1\n unsigned long long z = a;\n z *= b;\n#ifdef _MSC_VER\n unsigned long long x;\n _umul128(z, im, &x);\n#else\n unsigned long long x =\n (unsigned long long)(((unsigned __int128)(z)*im) >> 64);\n#endif\n unsigned int v = (unsigned int)(z - x * _m);\n if (_m <= v) v += _m;\n return v;\n }\n};\n\nstruct barrett2 {\n unsigned int _m;\n unsigned int _b;\n unsigned long long im;\n\n explicit barrett2(unsigned int m) {\n _m = m;\n _b = 32 - __builtin_clz(m);\n im = (unsigned long long)((((unsigned __int128)(1) << (_b + 64)) + m - 1) / m - ((unsigned __int128)(1) << 64));\n }\n\n unsigned int umod() const { return _m; }\n\n unsigned int mul(unsigned int a, unsigned int b) const {\n unsigned long long z = a;\n z *= b;\n unsigned long long x =\n (unsigned long long)((((unsigned __int128)(z)*im) >> 64) + z) >> _b;\n unsigned int v = (unsigned int)(z - x * _m);\n return v;\n }\n};\n\nstruct barrett3 {\n unsigned int _m;\n unsigned int _b;\n unsigned long long im;\n\n explicit barrett3(unsigned int m) {\n _m = m;\n _b = 31 - __builtin_clz(m);\n im = (unsigned long long)((((unsigned __int128)(1) << (_b + 64)) + m - 1) / m);\n }\n\n unsigned int umod() const { return _m; }\n\n unsigned int mul(unsigned int a, unsigned int b) const {\n unsigned long long z = a;\n z *= b;\n unsigned long long x =\n (unsigned long long)(((unsigned __int128)(z)*im) >> 64) >> _b;\n unsigned int v = (unsigned int)(z - x * _m);\n return v;\n }\n};\n\nstruct Timer {\n std::chrono::time_point start;\n std::chrono::time_point end;\n std::chrono::duration elapsed;\n\n void start_timer() { start = std::chrono::high_resolution_clock::now(); }\n void stop_timer() {\n end = std::chrono::high_resolution_clock::now();\n elapsed = end - start;\n }\n\n void print_elapsed(std::string title) {\n std::cout << title << \": \" << elapsed.count() << \" sec\" << std::endl;\n }\n};\n\nint main() {\n int n;\n std::cin >> n;\n {\n barrett b(n);\n\n Timer timer;\n timer.start_timer();\n unsigned long long sum = 0;\n \n for (int i = 0; i < n; i++) {\n sum += b.mul(i, i);\n // std::cout << i << \" \" << b.mul(i, i) << std::endl;\n }\n\n timer.stop_timer();\n timer.print_elapsed(\"barrett\");\n std::cout << sum << std::endl;\n }\n\n {\n barrett2 b(n);\n\n Timer timer;\n timer.start_timer();\n unsigned long long sum = 0;\n\n for (int i = 0; i < n; i++) {\n sum += b.mul(i, i);\n // std::cout << i << \" \" << b.mul(i, i) << std::endl;\n }\n\n timer.stop_timer();\n timer.print_elapsed(\"barrett2\");\n std::cout << sum << std::endl;\n }\n\n {\n barrett3 b(n);\n\n Timer timer;\n timer.start_timer();\n unsigned long long sum = 0;\n\n for (int i = 0; i < n; i++) {\n sum += b.mul(i, i);\n // std::cout << i << \" \" << b.mul(i, i) << std::endl;\n }\n\n timer.stop_timer();\n timer.print_elapsed(\"barrett3\");\n std::cout << sum << std::endl;\n 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