結果
問題 | No.2829 GCD Divination |
ユーザー |
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提出日時 | 2024-08-02 21:29:19 |
言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 246 ms / 2,000 ms |
コード長 | 20,671 bytes |
コンパイル時間 | 5,495 ms |
コンパイル使用メモリ | 320,476 KB |
実行使用メモリ | 48,024 KB |
最終ジャッジ日時 | 2024-08-02 21:29:29 |
合計ジャッジ時間 | 9,668 ms |
ジャッジサーバーID (参考情報) |
judge1 / judge4 |
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ファイルパターン | 結果 |
---|---|
other | AC * 35 |
ソースコード
#line 1 "/home/maspy/compro/library/my_template.hpp"#if defined(LOCAL)#include <my_template_compiled.hpp>#else// https://codeforces.com/blog/entry/96344#pragma GCC optimize("Ofast,unroll-loops")// いまの CF だとこれ入れると動かない?// #pragma GCC target("avx2,popcnt")#include <bits/stdc++.h>using namespace std;using ll = long long;using u32 = unsigned int;using u64 = unsigned long long;using i128 = __int128;using u128 = unsigned __int128;using f128 = __float128;template <class T>constexpr T infty = 0;template <>constexpr int infty<int> = 1'010'000'000;template <>constexpr ll infty<ll> = 2'020'000'000'000'000'000;template <>constexpr u32 infty<u32> = infty<int>;template <>constexpr u64 infty<u64> = infty<ll>;template <>constexpr i128 infty<i128> = i128(infty<ll>) * 2'000'000'000'000'000'000;template <>constexpr double infty<double> = infty<ll>;template <>constexpr long double infty<long double> = infty<ll>;using pi = pair<ll, ll>;using vi = vector<ll>;template <class T>using vc = vector<T>;template <class T>using vvc = vector<vc<T>>;template <class T>using vvvc = vector<vvc<T>>;template <class T>using vvvvc = vector<vvvc<T>>;template <class T>using vvvvvc = vector<vvvvc<T>>;template <class T>using pq = priority_queue<T>;template <class T>using pqg = priority_queue<T, vector<T>, greater<T>>;#define vv(type, name, h, ...) \vector<vector<type>> name(h, vector<type>(__VA_ARGS__))#define vvv(type, name, h, w, ...) \vector<vector<vector<type>>> name( \h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))#define vvvv(type, name, a, b, c, ...) \vector<vector<vector<vector<type>>>> name( \a, vector<vector<vector<type>>>( \b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))// https://trap.jp/post/1224/#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)#define overload4(a, b, c, d, e, ...) e#define overload3(a, b, c, d, ...) d#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)#define FOR_subset(t, s) \for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))#define all(x) x.begin(), x.end()#define len(x) ll(x.size())#define elif else if#define eb emplace_back#define mp make_pair#define mt make_tuple#define fi first#define se second#define stoi stollint popcnt(int x) { return __builtin_popcount(x); }int popcnt(u32 x) { return __builtin_popcount(x); }int popcnt(ll x) { return __builtin_popcountll(x); }int popcnt(u64 x) { return __builtin_popcountll(x); }int popcnt_mod_2(int x) { return __builtin_parity(x); }int popcnt_mod_2(u32 x) { return __builtin_parity(x); }int popcnt_mod_2(ll x) { return __builtin_parityll(x); }int popcnt_mod_2(u64 x) { return __builtin_parityll(x); }// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }template <typename T>T floor(T a, T b) {return a / b - (a % b && (a ^ b) < 0);}template <typename T>T ceil(T x, T y) {return floor(x + y - 1, y);}template <typename T>T bmod(T x, T y) {return x - y * floor(x, y);}template <typename T>pair<T, T> divmod(T x, T y) {T q = floor(x, y);return {q, x - q * y};}template <typename T, typename U>T SUM(const vector<U> &A) {T sm = 0;for (auto &&a: A) sm += a;return sm;}#define MIN(v) *min_element(all(v))#define MAX(v) *max_element(all(v))#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))#define UNIQUE(x) \sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()template <typename T>T POP(deque<T> &que) {T a = que.front();que.pop_front();return a;}template <typename T>T POP(pq<T> &que) {T a = que.top();que.pop();return a;}template <typename T>T POP(pqg<T> &que) {T a = que.top();que.pop();return a;}template <typename T>T POP(vc<T> &que) {T a = que.back();que.pop_back();return a;}template <typename F>ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {if (check_ok) assert(check(ok));while (abs(ok - ng) > 1) {auto x = (ng + ok) / 2;(check(x) ? ok : ng) = x;}return ok;}template <typename F>double binary_search_real(F check, double ok, double ng, int iter = 100) {FOR(iter) {double x = (ok + ng) / 2;(check(x) ? ok : ng) = x;}return (ok + ng) / 2;}template <class T, class S>inline bool chmax(T &a, const S &b) {return (a < b ? a = b, 1 : 0);}template <class T, class S>inline bool chmin(T &a, const S &b) {return (a > b ? a = b, 1 : 0);}// ? は -1vc<int> s_to_vi(const string &S, char first_char) {vc<int> A(S.size());FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }return A;}template <typename T, typename U>vector<T> cumsum(vector<U> &A, int off = 1) {int N = A.size();vector<T> B(N + 1);FOR(i, N) { B[i + 1] = B[i] + A[i]; }if (off == 0) B.erase(B.begin());return B;}// stable sorttemplate <typename T>vector<int> argsort(const vector<T> &A) {vector<int> ids(len(A));iota(all(ids), 0);sort(all(ids),[&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });return ids;}// A[I[0]], A[I[1]], ...template <typename T>vc<T> rearrange(const vc<T> &A, const vc<int> &I) {vc<T> B(len(I));FOR(i, len(I)) B[i] = A[I[i]];return B;}template <typename T, typename... Vectors>vc<T> concat(vc<T> &first, const Vectors &... others) {vc<T> res = first;(res.insert(res.end(), others.begin(), others.end()), ...);return res;}#endif#line 1 "/home/maspy/compro/library/other/io.hpp"#define FASTIO#include <unistd.h>// https://judge.yosupo.jp/submission/21623namespace fastio {static constexpr uint32_t SZ = 1 << 17;char ibuf[SZ];char obuf[SZ];char out[100];// pointer of ibuf, obufuint32_t pil = 0, pir = 0, por = 0;struct Pre {char num[10000][4];constexpr Pre() : num() {for (int i = 0; i < 10000; i++) {int n = i;for (int j = 3; j >= 0; j--) {num[i][j] = n % 10 | '0';n /= 10;}}}} constexpr pre;inline void load() {memcpy(ibuf, ibuf + pil, pir - pil);pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);pil = 0;if (pir < SZ) ibuf[pir++] = '\n';}inline void flush() {fwrite(obuf, 1, por, stdout);por = 0;}void rd(char &c) {do {if (pil + 1 > pir) load();c = ibuf[pil++];} while (isspace(c));}void rd(string &x) {x.clear();char c;do {if (pil + 1 > pir) load();c = ibuf[pil++];} while (isspace(c));do {x += c;if (pil == pir) load();c = ibuf[pil++];} while (!isspace(c));}template <typename T>void rd_real(T &x) {string s;rd(s);x = stod(s);}template <typename T>void rd_integer(T &x) {if (pil + 100 > pir) load();char c;doc = ibuf[pil++];while (c < '-');bool minus = 0;if constexpr (is_signed<T>::value || is_same_v<T, i128>) {if (c == '-') { minus = 1, c = ibuf[pil++]; }}x = 0;while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; }if constexpr (is_signed<T>::value || is_same_v<T, i128>) {if (minus) x = -x;}}void rd(int &x) { rd_integer(x); }void rd(ll &x) { rd_integer(x); }void rd(i128 &x) { rd_integer(x); }void rd(u32 &x) { rd_integer(x); }void rd(u64 &x) { rd_integer(x); }void rd(u128 &x) { rd_integer(x); }void rd(double &x) { rd_real(x); }void rd(long double &x) { rd_real(x); }void rd(f128 &x) { rd_real(x); }template <class T, class U>void rd(pair<T, U> &p) {return rd(p.first), rd(p.second);}template <size_t N = 0, typename T>void rd_tuple(T &t) {if constexpr (N < std::tuple_size<T>::value) {auto &x = std::get<N>(t);rd(x);rd_tuple<N + 1>(t);}}template <class... T>void rd(tuple<T...> &tpl) {rd_tuple(tpl);}template <size_t N = 0, typename T>void rd(array<T, N> &x) {for (auto &d: x) rd(d);}template <class T>void rd(vc<T> &x) {for (auto &d: x) rd(d);}void read() {}template <class H, class... T>void read(H &h, T &... t) {rd(h), read(t...);}void wt(const char c) {if (por == SZ) flush();obuf[por++] = c;}void wt(const string s) {for (char c: s) wt(c);}void wt(const char *s) {size_t len = strlen(s);for (size_t i = 0; i < len; i++) wt(s[i]);}template <typename T>void wt_integer(T x) {if (por > SZ - 100) flush();if (x < 0) { obuf[por++] = '-', x = -x; }int outi;for (outi = 96; x >= 10000; outi -= 4) {memcpy(out + outi, pre.num[x % 10000], 4);x /= 10000;}if (x >= 1000) {memcpy(obuf + por, pre.num[x], 4);por += 4;} else if (x >= 100) {memcpy(obuf + por, pre.num[x] + 1, 3);por += 3;} else if (x >= 10) {int q = (x * 103) >> 10;obuf[por] = q | '0';obuf[por + 1] = (x - q * 10) | '0';por += 2;} elseobuf[por++] = x | '0';memcpy(obuf + por, out + outi + 4, 96 - outi);por += 96 - outi;}template <typename T>void wt_real(T x) {ostringstream oss;oss << fixed << setprecision(15) << double(x);string s = oss.str();wt(s);}void wt(int x) { wt_integer(x); }void wt(ll x) { wt_integer(x); }void wt(i128 x) { wt_integer(x); }void wt(u32 x) { wt_integer(x); }void wt(u64 x) { wt_integer(x); }void wt(u128 x) { wt_integer(x); }void wt(double x) { wt_real(x); }void wt(long double x) { wt_real(x); }void wt(f128 x) { wt_real(x); }template <class T, class U>void wt(const pair<T, U> val) {wt(val.first);wt(' ');wt(val.second);}template <size_t N = 0, typename T>void wt_tuple(const T t) {if constexpr (N < std::tuple_size<T>::value) {if constexpr (N > 0) { wt(' '); }const auto x = std::get<N>(t);wt(x);wt_tuple<N + 1>(t);}}template <class... T>void wt(tuple<T...> tpl) {wt_tuple(tpl);}template <class T, size_t S>void wt(const array<T, S> val) {auto n = val.size();for (size_t i = 0; i < n; i++) {if (i) wt(' ');wt(val[i]);}}template <class T>void wt(const vector<T> val) {auto n = val.size();for (size_t i = 0; i < n; i++) {if (i) wt(' ');wt(val[i]);}}void print() { wt('\n'); }template <class Head, class... Tail>void print(Head &&head, Tail &&... tail) {wt(head);if (sizeof...(Tail)) wt(' ');print(forward<Tail>(tail)...);}// gcc expansion. called automaticall after main.void __attribute__((destructor)) _d() { flush(); }} // namespace fastiousing fastio::read;using fastio::print;using fastio::flush;#if defined(LOCAL)#define SHOW(...) \SHOW_IMPL(__VA_ARGS__, SHOW4, SHOW3, SHOW2, SHOW1)(__VA_ARGS__)#define SHOW_IMPL(_1, _2, _3, _4, NAME, ...) NAME#define SHOW1(x) print(#x, "=", (x)), flush()#define SHOW2(x, y) print(#x, "=", (x), #y, "=", (y)), flush()#define SHOW3(x, y, z) print(#x, "=", (x), #y, "=", (y), #z, "=", (z)), flush()#define SHOW4(x, y, z, w) \print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w)), flush()#else#define SHOW(...)#endif#define INT(...) \int __VA_ARGS__; \read(__VA_ARGS__)#define LL(...) \ll __VA_ARGS__; \read(__VA_ARGS__)#define U32(...) \u32 __VA_ARGS__; \read(__VA_ARGS__)#define U64(...) \u64 __VA_ARGS__; \read(__VA_ARGS__)#define STR(...) \string __VA_ARGS__; \read(__VA_ARGS__)#define CHAR(...) \char __VA_ARGS__; \read(__VA_ARGS__)#define DBL(...) \double __VA_ARGS__; \read(__VA_ARGS__)#define VEC(type, name, size) \vector<type> name(size); \read(name)#define VV(type, name, h, w) \vector<vector<type>> name(h, vector<type>(w)); \read(name)void YES(bool t = 1) { print(t ? "YES" : "NO"); }void NO(bool t = 1) { YES(!t); }void Yes(bool t = 1) { print(t ? "Yes" : "No"); }void No(bool t = 1) { Yes(!t); }void yes(bool t = 1) { print(t ? "yes" : "no"); }void no(bool t = 1) { yes(!t); }#line 3 "main.cpp"#line 2 "/home/maspy/compro/library/nt/factor.hpp"#line 2 "/home/maspy/compro/library/random/base.hpp"u64 RNG_64() {static uint64_t x_= uint64_t(chrono::duration_cast<chrono::nanoseconds>(chrono::high_resolution_clock::now().time_since_epoch()).count())* 10150724397891781847ULL;x_ ^= x_ << 7;return x_ ^= x_ >> 9;}u64 RNG(u64 lim) { return RNG_64() % lim; }ll RNG(ll l, ll r) { return l + RNG_64() % (r - l); }#line 2 "/home/maspy/compro/library/mod/mongomery_modint.hpp"// odd mod.// x の代わりに rx を持つtemplate <int id, typename U1, typename U2>struct Mongomery_modint {using mint = Mongomery_modint;inline static U1 m, r, n2;static constexpr int W = numeric_limits<U1>::digits;static void set_mod(U1 mod) {assert(mod & 1 && mod <= U1(1) << (W - 2));m = mod, n2 = -U2(m) % m, r = m;FOR(5) r *= 2 - m * r;r = -r;assert(r * m == U1(-1));}static U1 reduce(U2 b) { return (b + U2(U1(b) * r) * m) >> W; }U1 x;Mongomery_modint() : x(0) {}Mongomery_modint(U1 x) : x(reduce(U2(x) * n2)){};U1 val() const {U1 y = reduce(x);return y >= m ? y - m : y;}mint &operator+=(mint y) {x = ((x += y.x) >= m ? x - m : x);return *this;}mint &operator-=(mint y) {x -= (x >= y.x ? y.x : y.x - m);return *this;}mint &operator*=(mint y) {x = reduce(U2(x) * y.x);return *this;}mint operator+(mint y) const { return mint(*this) += y; }mint operator-(mint y) const { return mint(*this) -= y; }mint operator*(mint y) const { return mint(*this) *= y; }bool operator==(mint y) const {return (x >= m ? x - m : x) == (y.x >= m ? y.x - m : y.x);}bool operator!=(mint y) const { return not operator==(y); }mint pow(ll n) const {assert(n >= 0);mint y = 1, z = *this;for (; n; n >>= 1, z *= z)if (n & 1) y *= z;return y;}};template <int id>using Mongomery_modint_32 = Mongomery_modint<id, u32, u64>;template <int id>using Mongomery_modint_64 = Mongomery_modint<id, u64, u128>;#line 3 "/home/maspy/compro/library/nt/primetest.hpp"bool primetest(const u64 x) {assert(x < u64(1) << 62);if (x == 2 or x == 3 or x == 5 or x == 7) return true;if (x % 2 == 0 or x % 3 == 0 or x % 5 == 0 or x % 7 == 0) return false;if (x < 121) return x > 1;const u64 d = (x - 1) >> lowbit(x - 1);using mint = Mongomery_modint_64<202311020>;mint::set_mod(x);const mint one(u64(1)), minus_one(x - 1);auto ok = [&](u64 a) -> bool {auto y = mint(a).pow(d);u64 t = d;while (y != one && y != minus_one && t != x - 1) y *= y, t <<= 1;if (y != minus_one && t % 2 == 0) return false;return true;};if (x < (u64(1) << 32)) {for (u64 a: {2, 7, 61})if (!ok(a)) return false;} else {for (u64 a: {2, 325, 9375, 28178, 450775, 9780504, 1795265022}) {if (!ok(a)) return false;}}return true;}#line 5 "/home/maspy/compro/library/nt/factor.hpp"template <typename mint>ll rho(ll n, ll c) {assert(n > 1);const mint cc(c);auto f = [&](mint x) { return x * x + cc; };mint x = 1, y = 2, z = 1, q = 1;ll g = 1;const ll m = 1LL << (__lg(n) / 5);for (ll r = 1; g == 1; r <<= 1) {x = y;FOR(r) y = f(y);for (ll k = 0; k < r && g == 1; k += m) {z = y;FOR(min(m, r - k)) y = f(y), q *= x - y;g = gcd(q.val(), n);}}if (g == n) do {z = f(z);g = gcd((x - z).val(), n);} while (g == 1);return g;}ll find_prime_factor(ll n) {assert(n > 1);if (primetest(n)) return n;FOR(100) {ll m = 0;if (n < (1 << 30)) {using mint = Mongomery_modint_32<20231025>;mint::set_mod(n);m = rho<mint>(n, RNG(0, n));} else {using mint = Mongomery_modint_64<20231025>;mint::set_mod(n);m = rho<mint>(n, RNG(0, n));}if (primetest(m)) return m;n = m;}assert(0);return -1;}// ソートしてくれるvc<pair<ll, int>> factor(ll n) {assert(n >= 1);vc<pair<ll, int>> pf;FOR(p, 2, 100) {if (p * p > n) break;if (n % p == 0) {ll e = 0;do { n /= p, e += 1; } while (n % p == 0);pf.eb(p, e);}}while (n > 1) {ll p = find_prime_factor(n);ll e = 0;do { n /= p, e += 1; } while (n % p == 0);pf.eb(p, e);}sort(all(pf));return pf;}vc<pair<ll, int>> factor_by_lpf(ll n, vc<int>& lpf) {vc<pair<ll, int>> res;while (n > 1) {int p = lpf[n];int e = 0;while (n % p == 0) {n /= p;++e;}res.eb(p, e);}return res;}#line 2 "/home/maspy/compro/library/nt/divisors.hpp"// sort はしないvc<ll> divisors_by_pf(const vc<pair<ll, int>>& pf) {vi div = {1};for (auto&& [p, e]: pf) {ll n = len(div);ll pp = 1;FOR3(i, 1, e + 1) {pp *= p;FOR(j, n) div.eb(div[j] * pp);}}return div;}// sort はしないvc<ll> divisors(ll N) {auto pf = factor(N);return divisors_by_pf(pf);}// sort はしないvc<ll> divisors_by_lpf(ll N, vc<int>& lpf) {auto pf = factor_by_lpf(N, lpf);return divisors_by_pf(pf);}#line 2 "/home/maspy/compro/library/nt/primetable.hpp"template <typename T = int>vc<T> primetable(int LIM) {++LIM;const int S = 32768;static int done = 2;static vc<T> primes = {2}, sieve(S + 1);if (done < LIM) {done = LIM;primes = {2}, sieve.assign(S + 1, 0);const int R = LIM / 2;primes.reserve(int(LIM / log(LIM) * 1.1));vc<pair<int, int>> cp;for (int i = 3; i <= S; i += 2) {if (!sieve[i]) {cp.eb(i, i * i / 2);for (int j = i * i; j <= S; j += 2 * i) sieve[j] = 1;}}for (int L = 1; L <= R; L += S) {array<bool, S> block{};for (auto& [p, idx]: cp)for (int i = idx; i < S + L; idx = (i += p)) block[i - L] = 1;FOR(i, min(S, R - L)) if (!block[i]) primes.eb((L + i) * 2 + 1);}}int k = LB(primes, LIM + 1);return {primes.begin(), primes.begin() + k};}#line 3 "/home/maspy/compro/library/nt/zeta.hpp"template <typename T>void divisor_zeta(vc<T>& A) {assert(A[0] == 0);int N = len(A) - 1;auto P = primetable(N);for (auto&& p: P) { FOR3(x, 1, N / p + 1) A[p * x] += A[x]; }}template <typename T>void divisor_mobius(vc<T>& A) {assert(A[0] == 0);int N = len(A) - 1;auto P = primetable(N);for (auto&& p: P) { FOR3_R(x, 1, N / p + 1) A[p * x] -= A[x]; }}template <typename T>void multiplier_zeta(vc<T>& A) {assert(A[0] == 0);int N = len(A) - 1;auto P = primetable(N);for (auto&& p: P) { FOR3_R(x, 1, N / p + 1) A[x] += A[p * x]; }}template <typename T>void multiplier_mobius(vc<T>& A) {assert(A[0] == 0);int N = len(A) - 1;auto P = primetable(N);for (auto&& p: P) { FOR3(x, 1, N / p + 1) A[x] -= A[p * x]; }}#line 3 "/home/maspy/compro/library/nt/euler_phi.hpp"ll euler_phi(ll n) {auto pf = factor(n);for (auto&& [p, e]: pf) n -= n / p;return n;}template <typename T>vc<T> euler_phi_table(ll n) {vc<T> A(n + 1);FOR(i, 1, n + 1) A[i] = T(i);divisor_mobius(A);return A;}#line 6 "main.cpp"using Re = double;void solve() {LL(N);vc<int> phi = euler_phi_table<int>(N);SHOW(phi);vi D = divisors(N);sort(all(D));ll n = len(D);vc<Re> dp(n);dp[n - 1] = 1;Re ANS = 0;FOR_R(i, 1, n) {ll d = D[i];Re loop = 1.0 / d;ANS += dp[i] / (1.0 - loop);FOR(j, i) {ll e = D[j];if (d % e != 0) continue;Re p = Re(phi[d / e]) / (d - 1);SHOW(d, e, p);dp[j] += dp[i] * p;}}SHOW(dp);print(ANS);}signed main() {int T = 1;// INT(T);FOR(T) solve();return 0;}