#line 1 ".lib/template.hpp" #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define allof(obj) (obj).begin(), (obj).end() #define range(i, l, r) for(int i=l;i>1)|y_bit)) #define bit_kth(i, k) ((i >> k)&1) #define bit_highest(i) (i?63-__builtin_clzll(i):-1) #define bit_lowest(i) (i?__builtin_ctzll(i):-1) #define sleepms(t) std::this_thread::sleep_for(std::chrono::milliseconds(t)) using ll = long long; using ld = long double; using ul = uint64_t; using pi = std::pair; using pl = std::pair; using namespace std; template std::ostream &operator<<(std::ostream &dest, const std::pair &p){ dest << p.first << ' ' << p.second; return dest; } template std::ostream &operator<<(std::ostream &dest, const std::vector> &v){ int sz = v.size(); if(sz==0) return dest; for(int i=0;i std::ostream &operator<<(std::ostream &dest, const std::vector &v){ int sz = v.size(); if(sz==0) return dest; for(int i=0;i std::ostream &operator<<(std::ostream &dest, const std::array &v){ if(sz==0) return dest; for(int i=0;i std::ostream &operator<<(std::ostream &dest, const std::set &v){ for(auto itr=v.begin();itr!=v.end();){ dest << *itr; itr++; if(itr!=v.end()) dest << ' '; } return dest; } template std::ostream &operator<<(std::ostream &dest, const std::map &v){ for(auto itr=v.begin();itr!=v.end();){ dest << '(' << itr->first << ", " << itr->second << ')'; itr++; if(itr!=v.end()) dest << '\n'; } return dest; } std::ostream &operator<<(std::ostream &dest, __int128_t value) { std::ostream::sentry s(dest); if (s) { __uint128_t tmp = value < 0 ? -value : value; char buffer[128]; char *d = std::end(buffer); do { --d; *d = "0123456789"[tmp % 10]; tmp /= 10; } while (tmp != 0); if (value < 0) { --d; *d = '-'; } int len = std::end(buffer) - d; if (dest.rdbuf()->sputn(d, len) != len) { dest.setstate(std::ios_base::badbit); } } return dest; } template vector make_vec(size_t sz, T val){return std::vector(sz, val);} template auto make_vec(size_t sz, Tail ...tail){ return std::vector(tail...))>(sz, make_vec(tail...)); } template vector read_vec(size_t sz){ std::vector v(sz); for(int i=0;i<(int)sz;i++) std::cin >> v[i]; return v; } template auto read_vec(size_t sz, Tail ...tail){ auto v = std::vector(tail...))>(sz); for(int i=0;i<(int)sz;i++) v[i] = read_vec(tail...); return v; } void io_init(){ std::cin.tie(nullptr); std::ios::sync_with_stdio(false); } #line 2 "a.cpp" /* ll solve_small(int a, int b, int c, int d, int e, int f){ } void solve(){ int a, b, c, d, e, f; std::cin >> a >> b >> c >> d >> e >> f; // (1) (2) (3) (4) // # # # # # # // # # # # # # // 1回で同じ位置の異なる形 // 2回で上下左右に1個ずらした同型 // 1回で // (2, 3, 4) -> 2回で右上に1個ずらした(1, 2, 4) // (1, 3, 4) -> 2回で右下に1個ずらした() // ... } */ struct four_square_theorem{ int n; std::vector A; std::vector sz; // 0 <= i < Nについて以下のテーブルを作る // sum(A) = iを満たしlen(A)が最小(常に4つ以下になる) // O(N√N) void init(int _n){ n = _n; A.resize(n, -1); sz.resize(n, 5); sz[0] = 0; for(int i = 1; i < n; i++){ for(int j = 1; j * j <= i; j++){ if(sz[i - j * j] + 1 < sz[i]){ A[i] = j; sz[i] = sz[i - j * j] + 1; } } } } four_square_theorem(int _n){ init(_n); } // x = ∑A[i]^2 を満たす要素数最小のA(高々4つ) std::vector get_square(int x){ assert(n); assert(0 <= x && x < n); std::vector ret; while(x){ int y = A[x]; ret.push_back(y); x -= y * y; } return ret; } // x = ∑A[i]^2 を満たすA(要素数最小とは限らない, N = 10^5, x < 10^18なら高々6要素になる) // @param x <= 10^18 std::vector get_square_large(unsigned long long x){ std::vector ret; while(n <= x){ unsigned long long y = sqrtl(x); ret.push_back(y); x -= y * y; } while(x){ int y = A[x]; ret.push_back(y); x -= y * y; } return ret; } // x = ∑ A[i] * (A[i] + 1) / 2 を満たすA(3つ以下) std::vector get_trianglar(int x){ auto v = get_square(8 * x + 3); assert(v.size() == 3); std::vector ret; for(int i = 0; i < 3; i++) if(v[i] != 1) ret.push_back(v[i] / 2); return ret; } // x = ∑ A[i] * (A[i] + 1) / 2 を満たすA(要素数最小とは限らない, N = 10^5, x < 10^18なら高々5要素になる) // @param x <= 10^18 std::vector get_trianglar_large(unsigned long long x){ std::vector ret; while(n <= 8 * x + 3){ unsigned long long y = sqrtl(2 * x); while(y * (y + 1) > 2 * x) y--; ret.push_back(y); x -= (y & 1 ? y * ((y >> 1) + 1) : (y >> 1) * (y + 1)); } auto v = get_square(8 * x + 3); for(int i = 0; i < 3; i++) if(v[i] != 1) ret.push_back(v[i] / 2); return ret; } }; // ピタゴラス数について // a^2 + b^2 = c^3を満たす自然数の組(a, b, c)をピタゴラス数と呼ぶ // bが偶数, a, cが奇数でなければならない // 自然数x, y(x > y)を用いて(a, b, c) = (x^2 - y^2, 2xy, x^2 + y^2)を表すことができる  int main(){ io_init(); ll S; std::cin >> S; four_square_theorem f(100000); auto ans = f.get_square_large(S); range(i, 0, ans.size()) ans[i] *= ans[i]; std::cout << ans.size() << '\n'; std::cout << ans << '\n'; }