/** * date : 2023-12-01 00:22:18 * author : Nyaan */ #define NDEBUG using namespace std; // intrinstic #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include // utility namespace Nyaan { using ll = long long; using i64 = long long; using u64 = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; template using V = vector; template using VV = vector>; using vi = vector; using vl = vector; using vd = V; using vs = V; using vvi = vector>; using vvl = vector>; template using minpq = priority_queue, greater>; template struct P : pair { template P(Args... args) : pair(args...) {} using pair::first; using pair::second; P &operator+=(const P &r) { first += r.first; second += r.second; return *this; } P &operator-=(const P &r) { first -= r.first; second -= r.second; return *this; } P &operator*=(const P &r) { first *= r.first; second *= r.second; return *this; } template P &operator*=(const S &r) { first *= r, second *= r; return *this; } P operator+(const P &r) const { return P(*this) += r; } P operator-(const P &r) const { return P(*this) -= r; } P operator*(const P &r) const { return P(*this) *= r; } template P operator*(const S &r) const { return P(*this) *= r; } P operator-() const { return P{-first, -second}; } }; using pl = P; using pi = P; using vp = V; constexpr int inf = 1001001001; constexpr long long infLL = 4004004004004004004LL; template int sz(const T &t) { return t.size(); } template inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; } template inline T Max(const vector &v) { return *max_element(begin(v), end(v)); } template inline T Min(const vector &v) { return *min_element(begin(v), end(v)); } template inline long long Sum(const vector &v) { return accumulate(begin(v), end(v), 0LL); } template int lb(const vector &v, const T &a) { return lower_bound(begin(v), end(v), a) - begin(v); } template int ub(const vector &v, const T &a) { return upper_bound(begin(v), end(v), a) - begin(v); } constexpr long long TEN(int n) { long long ret = 1, x = 10; for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1); return ret; } template pair mkp(const T &t, const U &u) { return make_pair(t, u); } template vector mkrui(const vector &v, bool rev = false) { vector ret(v.size() + 1); if (rev) { for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1]; } else { for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i]; } return ret; }; template vector mkuni(const vector &v) { vector ret(v); sort(ret.begin(), ret.end()); ret.erase(unique(ret.begin(), ret.end()), ret.end()); return ret; } template vector mkord(int N, F f) { vector ord(N); iota(begin(ord), end(ord), 0); sort(begin(ord), end(ord), f); return ord; } template vector mkinv(vector &v) { int max_val = *max_element(begin(v), end(v)); vector inv(max_val + 1, -1); for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i; return inv; } vector mkiota(int n) { vector ret(n); iota(begin(ret), end(ret), 0); return ret; } template T mkrev(const T &v) { T w{v}; reverse(begin(w), end(w)); return w; } template bool nxp(vector &v) { return next_permutation(begin(v), end(v)); } // 返り値の型は入力の T に依存 // i 要素目 : [0, a[i]) template vector> product(const vector &a) { vector> ret; vector v; auto dfs = [&](auto rc, int i) -> void { if (i == (int)a.size()) { ret.push_back(v); return; } for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back(); }; dfs(dfs, 0); return ret; } // F : function(void(T&)), mod を取る操作 // T : 整数型のときはオーバーフローに注意する template T Power(T a, long long n, const T &I, const function &f) { T res = I; for (; n; f(a = a * a), n >>= 1) { if (n & 1) f(res = res * a); } return res; } // T : 整数型のときはオーバーフローに注意する template T Power(T a, long long n, const T &I = T{1}) { return Power(a, n, I, function{[](T &) -> void {}}); } template T Rev(const T &v) { T res = v; reverse(begin(res), end(res)); return res; } template vector Transpose(const vector &v) { using U = typename T::value_type; int H = v.size(), W = v[0].size(); vector res(W, T(H, U{})); for (int i = 0; i < H; i++) { for (int j = 0; j < W; j++) { res[j][i] = v[i][j]; } } return res; } template vector Rotate(const vector &v, int clockwise = true) { using U = typename T::value_type; int H = v.size(), W = v[0].size(); vector res(W, T(H, U{})); for (int i = 0; i < H; i++) { for (int j = 0; j < W; j++) { if (clockwise) { res[W - 1 - j][i] = v[i][j]; } else { res[j][H - 1 - i] = v[i][j]; } } } return res; } } // namespace Nyaan // bit operation namespace Nyaan { __attribute__((target("popcnt"))) inline int popcnt(const u64 &a) { return _mm_popcnt_u64(a); } inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; } template inline int gbit(const T &a, int i) { return (a >> i) & 1; } template inline void sbit(T &a, int i, bool b) { if (gbit(a, i) != b) a ^= T(1) << i; } constexpr long long PW(int n) { return 1LL << n; } constexpr long long MSK(int n) { return (1LL << n) - 1; } } // namespace Nyaan // inout namespace Nyaan { template ostream &operator<<(ostream &os, const pair &p) { os << p.first << " " << p.second; return os; } template istream &operator>>(istream &is, pair &p) { is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const vector &v) { int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template istream &operator>>(istream &is, vector &v) { for (auto &x : v) is >> x; return is; } istream &operator>>(istream &is, __int128_t &x) { string S; is >> S; x = 0; int flag = 0; for (auto &c : S) { if (c == '-') { flag = true; continue; } x *= 10; x += c - '0'; } if (flag) x = -x; return is; } istream &operator>>(istream &is, __uint128_t &x) { string S; is >> S; x = 0; for (auto &c : S) { x *= 10; x += c - '0'; } return is; } ostream &operator<<(ostream &os, __int128_t x) { if (x == 0) return os << 0; if (x < 0) os << '-', x = -x; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } ostream &operator<<(ostream &os, __uint128_t x) { if (x == 0) return os << 0; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } void in() {} template void in(T &t, U &...u) { cin >> t; in(u...); } void out() { cout << "\n"; } template void out(const T &t, const U &...u) { cout << t; if (sizeof...(u)) cout << sep; out(u...); } struct IoSetupNya { IoSetupNya() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7); } } iosetupnya; } // namespace Nyaan // debug #ifdef NyaanDebug #define trc(...) (void(0)) #else #define trc(...) (void(0)) #endif #ifdef NyaanLocal #define trc2(...) (void(0)) #else #define trc2(...) (void(0)) #endif // macro #define each(x, v) for (auto&& x : v) #define each2(x, y, v) for (auto&& [x, y] : v) #define all(v) (v).begin(), (v).end() #define rep(i, N) for (long long i = 0; i < (long long)(N); i++) #define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--) #define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++) #define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--) #define reg(i, a, b) for (long long i = (a); i < (b); i++) #define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--) #define fi first #define se second #define ini(...) \ int __VA_ARGS__; \ in(__VA_ARGS__) #define inl(...) \ long long __VA_ARGS__; \ in(__VA_ARGS__) #define ins(...) \ string __VA_ARGS__; \ in(__VA_ARGS__) #define in2(s, t) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i]); \ } #define in3(s, t, u) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i]); \ } #define in4(s, t, u, v) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i], v[i]); \ } #define die(...) \ do { \ Nyaan::out(__VA_ARGS__); \ return; \ } while (0) namespace Nyaan { void solve(); } int main() { Nyaan::solve(); } // using namespace std; using Real = long double; using Point = complex; using Points = vector; constexpr Real EPS = 1e-9; constexpr Real pi = 3.141592653589793238462643383279L; istream &operator>>(istream &is, Point &p) { Real a, b; is >> a >> b; p = Point(a, b); return is; } ostream &operator<<(ostream &os, Point &p) { return os << real(p) << " " << imag(p); } inline bool eq(Real a, Real b) { return fabs(b - a) < EPS; } int sign(Real a) { return eq(a, 0) ? 0 : a > 0 ? 1 : -1; } Point operator*(const Point &p, const Real &d) { return Point(real(p) * d, imag(p) * d); } namespace std { bool operator<(const Point &a, const Point &b) { return a.real() != b.real() ? a.real() < b.real() : a.imag() < b.imag(); } } // namespace std Real cross(const Point &a, const Point &b) { return real(a) * imag(b) - imag(a) * real(b); } Real dot(const Point &a, const Point &b) { return real(a) * real(b) + imag(a) * imag(b); } // ccw 点の進行方向 int ccw(const Point &a, Point b, Point c) { b = b - a, c = c - a; if (cross(b, c) > EPS) return +1; // 反時計回り if (cross(b, c) < -EPS) return -1; // 時計回り if (dot(b, c) < 0) return +2; // c-a-bの順で一直線 if (norm(b) < norm(c)) return -2; // a-b-cの順で一直線 return 0; // a-c-bの順で一直線 } // a-bベクトルとb-cベクトルのなす角度のうち小さい方を返す // (ベクトル同士のなす角、すなわち幾何でいうところの「外角」であることに注意!) // rem. 凸包に対して反時計回りにこの関数を適用すると、 // 凸包の大きさにかかわらず和が360度になる(いわゆる外角の和)(AGC021-B) Real get_angle(const Point &a, const Point &b, const Point &c) { const Point v(b - a), w(c - b); Real alpha = atan2(v.imag(), v.real()), beta = atan2(w.imag(), w.real()); if (alpha > beta) swap(alpha, beta); Real theta = (beta - alpha); return min(theta, 2 * acos(-1) - theta); } //  反時計回りである自己交差のない多角形のclass using Polygon = vector; // 凸包 Polygon convex_hull(vector ps) { int n = (int)ps.size(), k = 0; if (n <= 2) return ps; sort(ps.begin(), ps.end()); vector ch(2 * n); // 反時計周りに凸包を構築していく for (int i = 0; i < n; ch[k++] = ps[i++]) { // 条件分岐内はwhile(k >= 2 && ccw(ch[k-2],ch[k-1],ps[i]) != 1)と等価 while (k >= 2 && cross(ch[k - 1] - ch[k - 2], ps[i] - ch[k - 1]) < EPS) --k; } for (int i = n - 2, t = k + 1; i >= 0; ch[k++] = ps[i--]) { while (k >= t && cross(ch[k - 1] - ch[k - 2], ps[i] - ch[k - 1]) < EPS) --k; } ch.resize(k - 1); return ch; } // 多角形の面積 Real area(const Polygon &p) { Real A = 0; for (int i = 0; i < (int)p.size(); ++i) { A += cross(p[i], p[(i + 1) % p.size()]); } return A * 0.5; } struct Circle { Point p; Real r; Circle() = default; Circle(Point _p, Real _r) : p(_p), r(_r) {} }; using Circles = vector; int intersect(Circle c1, Circle c2) { if (c1.r < c2.r) swap(c1, c2); Real d = abs(c1.p - c2.p); if (c1.r + c2.r < d) return 4; if (eq(c1.r + c2.r, d)) return 3; if (c1.r - c2.r < d) return 2; if (eq(c1.r - c2.r, d)) return 1; return 0; } pair crosspoint(const Circle &c1, const Circle &c2) { Real d = abs(c1.p - c2.p); Real x = (c1.r * c1.r + d * d - c2.r * c2.r) / (2 * c1.r * d); if (abs(x) > 1) x = (x > 0 ? 1.0 : -1.0); Real a = acos(x); Real t = atan2(c2.p.imag() - c1.p.imag(), c2.p.real() - c1.p.real()); Point p1 = c1.p + Point(cos(t + a) * c1.r, sin(t + a) * c1.r); Point p2 = c1.p + Point(cos(t - a) * c1.r, sin(t - a) * c1.r); return {p1, p2}; } using namespace Nyaan; // c の向かいの角度 double yogen(double a, double b, double c) { return (a * a + b * b - c * c) / (2 * a * b); } void q() { ini(a, b, c); rep1(d, 200) rep1(e, 200) { if (c + b <= a + d + e) continue; if (min(b, c) + a + d + e <= max(b, c)) continue; double f = a + d + e; double t = acos(yogen(b, c, a + d + e)); Point A{0, 0}; Point B{double(b), 0}; Point C{c * cos(t), c * sin(t)}; double invf = 1.0 / f; Point D = (B * (a + e) + C * d) * invf; Point E = (B * e + C * (a + d)) * invf; double t1 = yogen(b, abs(A - D), d); double t2 = yogen(c, abs(A - E), e); if (d == 1 and e == 6) { trc(abs(C - E)); trc(abs(B - D)); trc(abs(B - C)); } if (abs(t1 - t2) < 1e-14) { out("Yes"); cerr << d << " " << e << endl; return; } } out("No"); } void Nyaan::solve() { int t = 1; // in(t); while (t--) q(); }