結果
問題 | No.1881 Everything is the same... |
ユーザー |
![]() |
提出日時 | 2022-10-27 11:05:13 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
WA
|
実行時間 | - |
コード長 | 24,328 bytes |
コンパイル時間 | 4,921 ms |
コンパイル使用メモリ | 272,200 KB |
最終ジャッジ日時 | 2025-02-08 13:14:24 |
ジャッジサーバーID (参考情報) |
judge3 / judge5 |
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ファイルパターン | 結果 |
---|---|
other | AC * 43 WA * 9 |
ソースコード
#line 1 "/home/maspy/compro/library/my_template.hpp"#pragma GCC optimize("Ofast")#pragma GCC optimize("unroll-loops")#include <bits/stdc++.h>using namespace std;using ll = long long;using pi = pair<ll, ll>;using vi = vector<ll>;using u32 = unsigned int;using u64 = unsigned long long;using i128 = __int128;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 vec(type, name, ...) vector<type> name(__VA_ARGS__)#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 FOR4_R(i, a, b, c) for (ll i = (b)-1; i >= ll(a); i -= (c))#define overload4(a, b, c, d, e, ...) e#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)#define FOR_R(...) \overload4(__VA_ARGS__, FOR4_R, 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 stolltemplate <typename T, typename U>T SUM(const vector<U> &A) {T sum = 0;for (auto &&a: A) sum += a;return sum;}#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())int 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); }// (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 pick(deque<T> &que) {T a = que.front();que.pop_front();return a;}template <typename T>T pick(pq<T> &que) {T a = que.top();que.pop();return a;}template <typename T>T pick(pqg<T> &que) {assert(que.size());T a = que.top();que.pop();return a;}template <typename T>T pick(vc<T> &que) {assert(que.size());T a = que.back();que.pop_back();return a;}template <typename T, typename U>T ceil(T x, U y) {return (x > 0 ? (x + y - 1) / y : x / y);}template <typename T, typename U>T floor(T x, U y) {return (x > 0 ? x / y : (x - y + 1) / y);}template <typename T, typename U>pair<T, T> divmod(T x, U y) {T q = floor(x, y);return {q, x - q * y};}template <typename F>ll binary_search(F check, ll ok, ll ng) {assert(check(ok));while (abs(ok - ng) > 1) {auto x = (ng + ok) / 2;tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, 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;tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, 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);}vc<int> s_to_vi(const string &S, char first_char) {vc<int> A(S.size());FOR(i, S.size()) { A[i] = S[i] - first_char; }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;}template <typename CNT, typename T>vc<CNT> bincount(const vc<T> &A, int size) {vc<CNT> C(size);for (auto &&x: A) { ++C[x]; }return C;}// stabletemplate <typename T>vector<int> argsort(const vector<T> &A) {vector<int> ids(A.size());iota(all(ids), 0);sort(all(ids),[&](int i, int j) { return A[i] < A[j] || (A[i] == A[j] && i < j); });return ids;}// A[I[0]], A[I[1]], ...template <typename T>vc<T> rearrange(const vc<T> &A, const vc<int> &I) {int n = len(I);vc<T> B(n);FOR(i, n) B[i] = A[I[i]];return B;}#line 1 "/home/maspy/compro/library/other/io.hpp"// based on yosupo's fastio#include <unistd.h>namespace detail {template <typename T, decltype(&T::is_modint) = &T::is_modint>std::true_type check_value(int);template <typename T>std::false_type check_value(long);} // namespace detailtemplate <typename T>struct is_modint : decltype(detail::check_value<T>(0)) {};template <typename T>using is_modint_t = enable_if_t<is_modint<T>::value>;template <typename T>using is_not_modint_t = enable_if_t<!is_modint<T>::value>;struct Scanner {FILE *fp;char line[(1 << 15) + 1];size_t st = 0, ed = 0;void reread() {memmove(line, line + st, ed - st);ed -= st;st = 0;ed += fread(line + ed, 1, (1 << 15) - ed, fp);line[ed] = '\0';}bool succ() {while (true) {if (st == ed) {reread();if (st == ed) return false;}while (st != ed && isspace(line[st])) st++;if (st != ed) break;}if (ed - st <= 50) {bool sep = false;for (size_t i = st; i < ed; i++) {if (isspace(line[i])) {sep = true;break;}}if (!sep) reread();}return true;}template <class T, enable_if_t<is_same<T, string>::value, int> = 0>bool read_single(T &ref) {if (!succ()) return false;while (true) {size_t sz = 0;while (st + sz < ed && !isspace(line[st + sz])) sz++;ref.append(line + st, sz);st += sz;if (!sz || st != ed) break;reread();}return true;}template <class T, enable_if_t<is_integral<T>::value, int> = 0>bool read_single(T &ref) {if (!succ()) return false;bool neg = false;if (line[st] == '-') {neg = true;st++;}ref = T(0);while (isdigit(line[st])) { ref = 10 * ref + (line[st++] & 0xf); }if (neg) ref = -ref;return true;}template <class T, is_modint_t<T> * = nullptr>bool read_single(T &ref) {long long val = 0;bool f = read_single(val);ref = T(val);return f;}bool read_single(double &ref) {string s;if (!read_single(s)) return false;ref = std::stod(s);return true;}bool read_single(char &ref) {string s;if (!read_single(s) || s.size() != 1) return false;ref = s[0];return true;}template <class T>bool read_single(vector<T> &ref) {for (auto &d: ref) {if (!read_single(d)) return false;}return true;}template <class T, class U>bool read_single(pair<T, U> &p) {return (read_single(p.first) && read_single(p.second));}template <class A, class B, class C>bool read_single(tuple<A, B, C> &p) {return (read_single(get<0>(p)) && read_single(get<1>(p))&& read_single(get<2>(p)));}template <class A, class B, class C, class D>bool read_single(tuple<A, B, C, D> &p) {return (read_single(get<0>(p)) && read_single(get<1>(p))&& read_single(get<2>(p)) && read_single(get<3>(p)));}void read() {}template <class H, class... T>void read(H &h, T &... t) {bool f = read_single(h);assert(f);read(t...);}Scanner(FILE *fp) : fp(fp) {}};struct Printer {Printer(FILE *_fp) : fp(_fp) {}~Printer() { flush(); }static constexpr size_t SIZE = 1 << 15;FILE *fp;char line[SIZE], small[50];size_t pos = 0;void flush() {fwrite(line, 1, pos, fp);pos = 0;}void write(const char &val) {if (pos == SIZE) flush();line[pos++] = val;}template <class T, enable_if_t<is_integral<T>::value, int> = 0>void write(T val) {if (pos > (1 << 15) - 50) flush();if (val == 0) {write('0');return;}if (val < 0) {write('-');val = -val; // todo min}size_t len = 0;while (val) {small[len++] = char(0x30 | (val % 10));val /= 10;}for (size_t i = 0; i < len; i++) { line[pos + i] = small[len - 1 - i]; }pos += len;}void write(const string &s) {for (char c: s) write(c);}void write(const char *s) {size_t len = strlen(s);for (size_t i = 0; i < len; i++) write(s[i]);}void write(const double &x) {ostringstream oss;oss << fixed << setprecision(15) << x;string s = oss.str();write(s);}void write(const long double &x) {ostringstream oss;oss << fixed << setprecision(15) << x;string s = oss.str();write(s);}template <class T, is_modint_t<T> * = nullptr>void write(T &ref) {write(ref.val);}template <class T>void write(const vector<T> &val) {auto n = val.size();for (size_t i = 0; i < n; i++) {if (i) write(' ');write(val[i]);}}template <class T, class U>void write(const pair<T, U> &val) {write(val.first);write(' ');write(val.second);}template <class A, class B, class C>void write(const tuple<A, B, C> &val) {auto &[a, b, c] = val;write(a), write(' '), write(b), write(' '), write(c);}template <class A, class B, class C, class D>void write(const tuple<A, B, C, D> &val) {auto &[a, b, c, d] = val;write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d);}template <class A, class B, class C, class D, class E>void write(const tuple<A, B, C, D, E> &val) {auto &[a, b, c, d, e] = val;write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d), write(' '), write(e);}template <class A, class B, class C, class D, class E, class F>void write(const tuple<A, B, C, D, E, F> &val) {auto &[a, b, c, d, e, f] = val;write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d), write(' '), write(e), write(' '), write(f);}template <class T, size_t S>void write(const array<T, S> &val) {auto n = val.size();for (size_t i = 0; i < n; i++) {if (i) write(' ');write(val[i]);}}void write(i128 val) {string s;bool negative = 0;if(val < 0){negative = 1;val = -val;}while (val) {s += '0' + int(val % 10);val /= 10;}if(negative) s += "-";reverse(all(s));if (len(s) == 0) s = "0";write(s);}};Scanner scanner = Scanner(stdin);Printer printer = Printer(stdout);void flush() { printer.flush(); }void print() { printer.write('\n'); }template <class Head, class... Tail>void print(Head &&head, Tail &&... tail) {printer.write(head);if (sizeof...(Tail)) printer.write(' ');print(forward<Tail>(tail)...);}void read() {}template <class Head, class... Tail>void read(Head &head, Tail &... tail) {scanner.read(head);read(tail...);}#define INT(...) \int __VA_ARGS__; \read(__VA_ARGS__)#define LL(...) \ll __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 2 "/home/maspy/compro/library/random/hash_vector.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/modint61.hpp"struct modint61 {static constexpr bool is_modint = true;static constexpr ll mod = (1LL << 61) - 1;ll val;constexpr modint61(const ll x = 0) : val(x) {while(val < 0) val += mod;while(val >= mod) val -= mod;}bool operator<(const modint61 &other) const {return val < other.val;} // To use std::mapbool operator==(const modint61 &p) const { return val == p.val; }bool operator!=(const modint61 &p) const { return val != p.val; }modint61 &operator+=(const modint61 &p) {if ((val += p.val) >= mod) val -= mod;return *this;}modint61 &operator-=(const modint61 &p) {if ((val += mod - p.val) >= mod) val -= mod;return *this;}modint61 &operator*=(const modint61 &p) {ll a = val, b = p.val;const ll MASK30 = (1LL << 30) - 1;const ll MASK31 = (1LL << 31) - 1;const ll MASK61 = (1LL << 61) - 1;ll au = a >> 31, ad = a & MASK31;ll bu = b >> 31, bd = b & MASK31;ll x = ad * bu + au * bd;ll xu = x >> 30, xd = x & MASK30;x = au * bu * 2 + xu + (xd << 31) + ad * bd;xu = x >> 61, xd = x & MASK61;x = xu + xd;if (x >= MASK61) x -= MASK61;val = x;return *this;}modint61 operator-() const { return modint61(get_mod() - val); }modint61 &operator/=(const modint61 &p) {*this *= p.inverse();return *this;}modint61 operator+(const modint61 &p) const { return modint61(*this) += p; }modint61 operator-(const modint61 &p) const { return modint61(*this) -= p; }modint61 operator*(const modint61 &p) const { return modint61(*this) *= p; }modint61 operator/(const modint61 &p) const { return modint61(*this) /= p; }modint61 inverse() const {ll a = val, b = mod, u = 1, v = 0, t;while (b > 0) {t = a / b;swap(a -= t * b, b), swap(u -= t * v, v);}return modint61(u);}modint61 pow(int64_t n) const {modint61 ret(1), mul(val);while (n > 0) {if (n & 1) ret = ret * mul;mul = mul * mul;n >>= 1;}return ret;}static constexpr ll get_mod() { return mod; }};#line 5 "/home/maspy/compro/library/random/hash_vector.hpp"template <typename T>ll hash_vector(vc<T> X) {using mint = modint61;static vc<mint> hash_base;int n = len(X);while (len(hash_base) <= n) { hash_base.eb(RNG(mint::get_mod())); }mint H = 0;FOR(i, n) H += hash_base[i] * mint(X[i]);H += hash_base[n];return H.val;}#line 2 "/home/maspy/compro/library/ds/hashmap.hpp"template <typename Val, int LOG = 20>struct HashMapLL {int N;ll* keys;Val* vals;vc<int> IDS;bitset<1 << LOG> used;const int shift;const uint64_t r = 11995408973635179863ULL;HashMapLL(): N(1 << LOG), keys(new ll[N]), vals(new Val[N]), shift(64 - __lg(N)) {}int hash(ll x) {static const uint64_t FIXED_RANDOM= std::chrono::steady_clock::now().time_since_epoch().count();return (uint64_t(x + FIXED_RANDOM) * r) >> shift;}int index(const ll& key) {int i = 0;for (i = hash(key); used[i] && keys[i] != key; (i += 1) &= (N - 1)) {}return i;}Val& operator[](const ll& key) {int i = index(key);if (!used[i]) IDS.eb(i), used[i] = 1, keys[i] = key, vals[i] = Val{};return vals[i];}Val get(const ll& key, Val default_value) {int i = index(key);if (!used[i]) return default_value;return vals[i];}bool contain(const ll& key) {int i = index(key);return used[i] && keys[i] == key;}bool count(const ll& key) {int i = index(key);return used[i] && keys[i] == key;}void reset() {for (auto&& i: IDS) used[i] = 0;IDS.clear();}vc<pair<ll, Val>> items() {vc<pair<ll, Val>> res;res.reserve(len(IDS));for (auto&& i: IDS) res.eb(keys[i], vals[i]);return res;}};template <typename KEY, typename VAL, int LOG>struct HashMap {HashMapLL<VAL, LOG> MP;function<ll(KEY)> f;HashMap(function<ll(KEY)> f) : MP(), f(f) {}int index(const KEY& key) { return MP.index(f(key)); }VAL& operator[](const KEY& key) { return MP[f(key)]; }bool contain(const KEY& key) { return MP.contain(f(key)); }bool count(const KEY& key) { return MP.count(f(key)); }void reset() { MP.reset(); }};#line 2 "/home/maspy/compro/library/nt/primetable.hpp"vc<ll> primetable(int LIM) {++LIM;const int S = 32768;static int done = 2;static vc<ll> 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<pi> 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/lpf_table.hpp"// [0, LIM], 0, 1 には -1 が入る。vc<int> lpf_table(ll LIM) {auto primes = primetable(LIM);vc<int> res(LIM + 1, -1);FOR_R(i, len(primes)) {auto p = primes[i];FOR3(j, 1, LIM / p + 1) res[p * j] = p;}return res;}#line 2 "/home/maspy/compro/library/nt/primetest.hpp"struct m64 {using i64 = int64_t;using u64 = uint64_t;using u128 = __uint128_t;inline static u64 m, r, n2; // r * m = -1 (mod 1<<64), n2 = 1<<128 (mod m)static void set_mod(u64 m) {assert(m < (1ull << 62));assert((m & 1) == 1);m64::m = m;n2 = -u128(m) % m;r = m;FOR(_, 5) r *= 2 - m * r;r = -r;assert(r * m == -1ull);}static u64 reduce(u128 b) { return (b + u128(u64(b) * r) * m) >> 64; }u64 x;m64() : x(0) {}m64(u64 x) : x(reduce(u128(x) * n2)){};u64 val() const {u64 y = reduce(x);return y >= m ? y - m : y;}m64 &operator+=(m64 y) {x += y.x - (m << 1);x = (i64(x) < 0 ? x + (m << 1) : x);return *this;}m64 &operator-=(m64 y) {x -= y.x;x = (i64(x) < 0 ? x + (m << 1) : x);return *this;}m64 &operator*=(m64 y) {x = reduce(u128(x) * y.x);return *this;}m64 operator+(m64 y) const { return m64(*this) += y; }m64 operator-(m64 y) const { return m64(*this) -= y; }m64 operator*(m64 y) const { return m64(*this) *= y; }bool operator==(m64 y) const {return (x >= m ? x - m : x) == (y.x >= m ? y.x - m : y.x);}bool operator!=(m64 y) const { return not operator==(y); }m64 pow(u64 n) const {m64 y = 1, z = *this;for (; n; n >>= 1, z *= z)if (n & 1) y *= z;return y;}};bool primetest(const uint64_t x) {using u64 = uint64_t;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) >> __builtin_ctzll(x - 1);m64::set_mod(x);const m64 one(1), minus_one(x - 1);auto ok = [&](u64 a) {auto y = m64(a).pow(d);u64 t = d;while (y != one and y != minus_one and t != x - 1) y *= y, t <<= 1;if (y != minus_one and t % 2 == 0) return false;return true;};if (x < (1ull << 32)) {for (u64 a: {2, 7, 61})if (not ok(a)) return false;} else {for (u64 a: {2, 325, 9375, 28178, 450775, 9780504, 1795265022}) {if (x <= a) return true;if (not ok(a)) return false;}}return true;}#line 3 "/home/maspy/compro/library/nt/factor.hpp"mt19937_64 rng_mt{random_device{}()};ll rnd(ll n) { return uniform_int_distribution<ll>(0, n - 1)(rng_mt); }ll rho(ll n, ll c) {m64::set_mod(n);assert(n > 1);const m64 cc(c);auto f = [&](m64 x) { return x * x + cc; };m64 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 and 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 = rho(n, rnd(n));if (primetest(m)) return m;n = m;}cerr << "failed" << endl;assert(false);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;FOR3(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 7 "main.cpp"void solve() {LL(N);VEC(ll, A, N);auto lpf = lpf_table(MAX(A));HashMapLL<int> MP;auto dfs = [&](auto& dfs, vc<int> A) -> int {while (len(A) && A.back() == 0) A.pop_back();if (len(A) == 0) return 0;ll h = hash_vector(A);if (MP.count(h)) return MP[h];vc<int> nxt;int n = len(A);A.eb(0);vc<int> B(n);auto gen = [&](auto& gen, int s) -> void {if (s == n) {if (SUM<int>(A) == SUM<int>(B)) return;nxt.eb(dfs(dfs, B));return;}FOR(x, A[s + 1], A[s] + 1) {B[s] = x;gen(gen, s + 1);}};gen(gen, 0);int K = len(nxt);vc<bool> used(K + 1);for (auto&& x: nxt) used[x] = 1;int mex = 0;while (used[mex]) ++mex;return (MP[h] = mex);};ll g = 0;for (auto&& a: A) {map<int, vc<int>> G;for (auto&& [p, e]: factor_by_lpf(a, lpf)) {if (p == 2) {if (e == 1) continue;G[2].eb(1);G[2].eb(e - 2);} else {// (p-1)p^{e-1}G[p].eb(e - 1);for (auto&& [q, f]: factor_by_lpf(p - 1, lpf)) { G[q].eb(f); }}}for (auto&& [p, E]: G) {sort(all(E));reverse(all(E));g ^= dfs(dfs, E);}}print(g == 0 ? "X" : "Y");}signed main() {cout << fixed << setprecision(15);ll T = 1;// LL(T);FOR(T) solve();return 0;}