結果
問題 | No.1291 小手調べ |
ユーザー |
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提出日時 | 2020-11-20 21:32:37 |
言語 | C++17(clang) (17.0.6 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 2 ms / 2,000 ms |
コード長 | 56,242 bytes |
コンパイル時間 | 4,117 ms |
コンパイル使用メモリ | 183,680 KB |
実行使用メモリ | 6,944 KB |
最終ジャッジ日時 | 2024-07-23 12:41:48 |
合計ジャッジ時間 | 4,131 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge5 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 1 |
other | AC * 4 |
コンパイルメッセージ
main.cpp:7:18: warning: '#pragma comment linker' ignored [-Wignored-pragmas] 7 | #pragma comment (linker, "/STACK:526000000") | ^ main.cpp:695:25: warning: unqualified call to 'std::move' [-Wunqualified-std-cast-call] 695 | auto c2 = convolution(move(a2), move(b2)); | ^ | std:: main.cpp:723:13: note: in instantiation of function template specialization 'atcoder::convolution<754974721U, long long, nullptr>' requested here 723 | auto c1 = convolution<MOD1>(a, b); | ^ main.cpp:695:35: warning: unqualified call to 'std::move' [-Wunqualified-std-cast-call] 695 | auto c2 = convolution(move(a2), move(b2)); | ^ | std:: main.cpp:695:25: warning: unqualified call to 'std::move' [-Wunqualified-std-cast-call] 695 | auto c2 = convolution(move(a2), move(b2)); | ^ | std:: main.cpp:724:13: note: in instantiation of function template specialization 'atcoder::convolution<167772161U, long long, nullptr>' requested here 724 | auto c2 = convolution<MOD2>(a, b); | ^ main.cpp:695:35: warning: unqualified call to 'std::move' [-Wunqualified-std-cast-call] 695 | auto c2 = convolution(move(a2), move(b2)); | ^ | std:: main.cpp:695:25: warning: unqualified call to 'std::move' [-Wunqualified-std-cast-call] 695 | auto c2 = convolution(move(a2), move(b2)); | ^ | std:: main.cpp:725:13: note: in instantiation of fun
ソースコード
#define _CRT_SECURE_NO_WARNINGS#define _USE_MATH_DEFINES#define _SILENCE_ALL_CXX17_DEPRECATION_WARNINGS#pragma GCC target("avx2")#pragma GCC optimize("O3")#pragma GCC optimize("unroll-loops")#pragma comment (linker, "/STACK:526000000")#include "bits/stdc++.h"/*AtCoder Compressed STL, licensed under public domain (cc0)Download Compressed: https://gist.github.com/yosupo06/ddd51afb727600fd95d9d8ad6c3c80c9based on AtCoder STL,Download: https://img.atcoder.jp/practice2/ac-library.zip*/#include <algorithm>#include <array>#ifdef _MSC_VER#include <intrin.h>#endifnamespace atcoder {namespace internal {int ceil_pow2(int n) {int x = 0;while ((1U << x) < (unsigned int)(n)) x++;return x;}int bsf(unsigned int n) {#ifdef _MSC_VERunsigned long index;_BitScanForward(&index, n);return index;#elsereturn __builtin_ctz(n);#endif}} // namespace internal} // namespace atcoder#include <utility>namespace atcoder {namespace internal {constexpr long long safe_mod(long long x, long long m) {x %= m;if (x < 0) x += m;return x;}struct barrett {unsigned int _m;unsigned long long im;barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}unsigned int umod() const { return _m; }unsigned int mul(unsigned int a, unsigned int b) const {unsigned long long z = a;z *= b;#ifdef _MSC_VERunsigned long long x;_umul128(z, im, &x);#elseunsigned long long x =(unsigned long long)(((unsigned __int128)(z)*im) >> 64);#endifunsigned int v = (unsigned int)(z - x * _m);if (_m <= v) v += _m;return v;}};constexpr long long pow_mod_constexpr(long long x, long long n, int m) {if (m == 1) return 0;unsigned int _m = (unsigned int)(m);unsigned long long r = 1;unsigned long long y = safe_mod(x, m);while (n) {if (n & 1) r = (r * y) % _m;y = (y * y) % _m;n >>= 1;}return r;}constexpr bool is_prime_constexpr(int n) {if (n <= 1) return false;if (n == 2 || n == 7 || n == 61) return true;if (n % 2 == 0) return false;long long d = n - 1;while (d % 2 == 0) d /= 2;int v[3] = { 2,7,61 };for (long long a : v) {long long t = d;long long y = pow_mod_constexpr(a, t, n);while (t != n - 1 && y != 1 && y != n - 1) {y = y * y % n;t <<= 1;}if (y != n - 1 && t % 2 == 0) {return false;}}return true;}template <int n> constexpr bool is_prime = is_prime_constexpr(n);constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {a = safe_mod(a, b);if (a == 0) return { b, 0 };long long s = b, t = a;long long m0 = 0, m1 = 1;while (t) {long long u = s / t;s -= t * u;m0 -= m1 * u; // |m1 * u| <= |m1| * s <= bauto tmp = s;s = t;t = tmp;tmp = m0;m0 = m1;m1 = tmp;}if (m0 < 0) m0 += b / s;return { s, m0 };}constexpr int primitive_root_constexpr(int m) {if (m == 2) return 1;if (m == 167772161) return 3;if (m == 469762049) return 3;if (m == 754974721) return 11;if (m == 998244353) return 3;int divs[20] = {};divs[0] = 2;int cnt = 1;int x = (m - 1) / 2;while (x % 2 == 0) x /= 2;for (int i = 3; (long long)(i)*i <= x; i += 2) {if (x % i == 0) {divs[cnt++] = i;while (x % i == 0) {x /= i;}}}if (x > 1) {divs[cnt++] = x;}for (int g = 2;; g++) {bool ok = true;for (int i = 0; i < cnt; i++) {if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {ok = false;break;}}if (ok) return g;}}template <int m> constexpr int primitive_root = primitive_root_constexpr(m);} // namespace internal} // namespace atcoder#include <cassert>#include <numeric>#include <type_traits>namespace atcoder {namespace internal {#ifndef _MSC_VERtemplate <class T>using is_signed_int128 =typename std::conditional<std::is_same<T, __int128_t>::value ||std::is_same<T, __int128>::value,std::true_type,std::false_type>::type;template <class T>using is_unsigned_int128 =typename std::conditional<std::is_same<T, __uint128_t>::value ||std::is_same<T, unsigned __int128>::value,std::true_type,std::false_type>::type;template <class T>using make_unsigned_int128 =typename std::conditional<std::is_same<T, __int128_t>::value,__uint128_t,unsigned __int128>;template <class T>using is_integral = typename std::conditional<std::is_integral<T>::value ||is_signed_int128<T>::value ||is_unsigned_int128<T>::value,std::true_type,std::false_type>::type;template <class T>using is_signed_int = typename std::conditional<(is_integral<T>::value&&std::is_signed<T>::value) ||is_signed_int128<T>::value,std::true_type,std::false_type>::type;template <class T>using is_unsigned_int =typename std::conditional<(is_integral<T>::value&&std::is_unsigned<T>::value) ||is_unsigned_int128<T>::value,std::true_type,std::false_type>::type;template <class T>using to_unsigned = typename std::conditional<is_signed_int128<T>::value,make_unsigned_int128<T>,typename std::conditional<std::is_signed<T>::value,std::make_unsigned<T>,std::common_type<T>>::type>::type;#elsetemplate <class T> using is_integral = typename std::is_integral<T>;template <class T>using is_signed_int =typename std::conditional<is_integral<T>::value&& std::is_signed<T>::value,std::true_type,std::false_type>::type;template <class T>using is_unsigned_int =typename std::conditional<is_integral<T>::value&&std::is_unsigned<T>::value,std::true_type,std::false_type>::type;template <class T>using to_unsigned = typename std::conditional<is_signed_int<T>::value,std::make_unsigned<T>,std::common_type<T>>::type;#endiftemplate <class T>using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;template <class T>using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;template <class T> using to_unsigned_t = typename to_unsigned<T>::type;} // namespace internal} // namespace atcoder#include <cassert>#include <numeric>#include <type_traits>#ifdef _MSC_VER#include <intrin.h>#endifnamespace atcoder {namespace internal {struct modint_base {};struct static_modint_base : modint_base {};template <class T> using is_modint = std::is_base_of<modint_base, T>;template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;} // namespace internaltemplate <int m, std::enable_if_t<(1 <= m)>* = nullptr>struct static_modint : internal::static_modint_base {using mint = static_modint;public:static constexpr int mod() { return m; }static mint raw(int v) {mint x;x._v = v;return x;}static_modint() : _v(0) {}template <class T, internal::is_signed_int_t<T>* = nullptr>static_modint(T v) {long long x = (long long)(v % (long long)(umod()));if (x < 0) x += umod();_v = (unsigned int)(x);}template <class T, internal::is_unsigned_int_t<T>* = nullptr>static_modint(T v) {_v = (unsigned int)(v % umod());}static_modint(bool v) { _v = ((unsigned int)(v) % umod()); }unsigned int val() const { return _v; }mint& operator++() {_v++;if (_v == umod()) _v = 0;return *this;}mint& operator--() {if (_v == 0) _v = umod();_v--;return *this;}mint operator++(int) {mint result = *this;++* this;return result;}mint operator--(int) {mint result = *this;--* this;return result;}mint& operator+=(const mint& rhs) {_v += rhs._v;if (_v >= umod()) _v -= umod();return *this;}mint& operator-=(const mint& rhs) {_v -= rhs._v;if (_v >= umod()) _v += umod();return *this;}mint& operator*=(const mint& rhs) {unsigned long long z = _v;z *= rhs._v;_v = (unsigned int)(z % umod());return *this;}mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }mint operator+() const { return *this; }mint operator-() const { return mint() - *this; }mint pow(long long n) const {assert(0 <= n);mint x = *this, r = 1;while (n) {if (n & 1) r *= x;x *= x;n >>= 1;}return r;}mint inv() const {if (prime) {assert(_v);return pow(umod() - 2);}else {auto eg = internal::inv_gcd(_v, m);assert(eg.first == 1);return eg.second;}}friend mint operator+(const mint& lhs, const mint& rhs) {return mint(lhs) += rhs;}friend mint operator-(const mint& lhs, const mint& rhs) {return mint(lhs) -= rhs;}friend mint operator*(const mint& lhs, const mint& rhs) {return mint(lhs) *= rhs;}friend mint operator/(const mint& lhs, const mint& rhs) {return mint(lhs) /= rhs;}friend bool operator==(const mint& lhs, const mint& rhs) {return lhs._v == rhs._v;}friend bool operator!=(const mint& lhs, const mint& rhs) {return lhs._v != rhs._v;}private:unsigned int _v;static constexpr unsigned int umod() { return m; }static constexpr bool prime = internal::is_prime<m>;};template <int id> struct dynamic_modint : internal::modint_base {using mint = dynamic_modint;public:static int mod() { return (int)(bt.umod()); }static void set_mod(int m) {assert(1 <= m);bt = internal::barrett(m);}static mint raw(int v) {mint x;x._v = v;return x;}dynamic_modint() : _v(0) {}template <class T, internal::is_signed_int_t<T>* = nullptr>dynamic_modint(T v) {long long x = (long long)(v % (long long)(mod()));if (x < 0) x += mod();_v = (unsigned int)(x);}template <class T, internal::is_unsigned_int_t<T>* = nullptr>dynamic_modint(T v) {_v = (unsigned int)(v % mod());}dynamic_modint(bool v) { _v = ((unsigned int)(v) % mod()); }unsigned int val() const { return _v; }mint& operator++() {_v++;if (_v == umod()) _v = 0;return *this;}mint& operator--() {if (_v == 0) _v = umod();_v--;return *this;}mint operator++(int) {mint result = *this;++* this;return result;}mint operator--(int) {mint result = *this;--* this;return result;}mint& operator+=(const mint& rhs) {_v += rhs._v;if (_v >= umod()) _v -= umod();return *this;}mint& operator-=(const mint& rhs) {_v += mod() - rhs._v;if (_v >= umod()) _v -= umod();return *this;}mint& operator*=(const mint& rhs) {_v = bt.mul(_v, rhs._v);return *this;}mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }mint operator+() const { return *this; }mint operator-() const { return mint() - *this; }mint pow(long long n) const {assert(0 <= n);mint x = *this, r = 1;while (n) {if (n & 1) r *= x;x *= x;n >>= 1;}return r;}mint inv() const {auto eg = internal::inv_gcd(_v, mod());assert(eg.first == 1);return eg.second;}friend mint operator+(const mint& lhs, const mint& rhs) {return mint(lhs) += rhs;}friend mint operator-(const mint& lhs, const mint& rhs) {return mint(lhs) -= rhs;}friend mint operator*(const mint& lhs, const mint& rhs) {return mint(lhs) *= rhs;}friend mint operator/(const mint& lhs, const mint& rhs) {return mint(lhs) /= rhs;}friend bool operator==(const mint& lhs, const mint& rhs) {return lhs._v == rhs._v;}friend bool operator!=(const mint& lhs, const mint& rhs) {return lhs._v != rhs._v;}private:unsigned int _v;static internal::barrett bt;static unsigned int umod() { return bt.umod(); }};template <int id> internal::barrett dynamic_modint<id>::bt = 998244353;using modint998244353 = static_modint<998244353>;using modint1000000007 = static_modint<1000000007>;using modint = dynamic_modint<-1>;namespace internal {template <class T>using is_static_modint = std::is_base_of<internal::static_modint_base, T>;template <class T>using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;template <class> struct is_dynamic_modint : public std::false_type {};template <int id>struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};template <class T>using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;} // namespace internal} // namespace atcoder#include <cassert>#include <type_traits>#include <vector>namespace atcoder {namespace internal {template <class mint, internal::is_static_modint_t<mint>* = nullptr>void butterfly(std::vector<mint>& a) {static constexpr int g = internal::primitive_root<mint::mod()>;int n = int(a.size());int h = internal::ceil_pow2(n);static bool first = true;static mint sum_e[30]; // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]if (first) {first = false;mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1int cnt2 = bsf(mint::mod() - 1);mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();for (int i = cnt2; i >= 2; i--) {es[i - 2] = e;ies[i - 2] = ie;e *= e;ie *= ie;}mint now = 1;for (int i = 0; i < cnt2 - 2; i++) {sum_e[i] = es[i] * now;now *= ies[i];}}for (int ph = 1; ph <= h; ph++) {int w = 1 << (ph - 1), p = 1 << (h - ph);mint now = 1;for (int s = 0; s < w; s++) {int offset = s << (h - ph + 1);for (int i = 0; i < p; i++) {auto l = a[i + offset];auto r = a[i + offset + p] * now;a[i + offset] = l + r;a[i + offset + p] = l - r;}now *= sum_e[bsf(~(unsigned int)(s))];}}}template <class mint, internal::is_static_modint_t<mint>* = nullptr>void butterfly_inv(std::vector<mint>& a) {static constexpr int g = internal::primitive_root<mint::mod()>;int n = int(a.size());int h = internal::ceil_pow2(n);static bool first = true;static mint sum_ie[30]; // sum_ie[i] = es[0] * ... * es[i - 1] * ies[i]if (first) {first = false;mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1int cnt2 = bsf(mint::mod() - 1);mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();for (int i = cnt2; i >= 2; i--) {es[i - 2] = e;ies[i - 2] = ie;e *= e;ie *= ie;}mint now = 1;for (int i = 0; i < cnt2 - 2; i++) {sum_ie[i] = ies[i] * now;now *= es[i];}}for (int ph = h; ph >= 1; ph--) {int w = 1 << (ph - 1), p = 1 << (h - ph);mint inow = 1;for (int s = 0; s < w; s++) {int offset = s << (h - ph + 1);for (int i = 0; i < p; i++) {auto l = a[i + offset];auto r = a[i + offset + p];a[i + offset] = l + r;a[i + offset + p] =(unsigned long long)(mint::mod() + l.val() - r.val()) *inow.val();}inow *= sum_ie[bsf(~(unsigned int)(s))];}}}} // namespace internaltemplate <class mint, internal::is_static_modint_t<mint>* = nullptr>std::vector<mint> convolution(std::vector<mint> a, std::vector<mint> b) {int n = int(a.size()), m = int(b.size());if (!n || !m) return {};if (std::min(n, m) <= 60) {if (n < m) {std::swap(n, m);std::swap(a, b);}std::vector<mint> ans(n + m - 1);for (int i = 0; i < n; i++) {for (int j = 0; j < m; j++) {ans[i + j] += a[i] * b[j];}}return ans;}int z = 1 << internal::ceil_pow2(n + m - 1);a.resize(z);internal::butterfly(a);b.resize(z);internal::butterfly(b);for (int i = 0; i < z; i++) {a[i] *= b[i];}internal::butterfly_inv(a);a.resize(n + m - 1);mint iz = mint(z).inv();for (int i = 0; i < n + m - 1; i++) a[i] *= iz;return a;}template <unsigned int mod = 998244353,class T,std::enable_if_t<internal::is_integral<T>::value>* = nullptr>std::vector<T> convolution(const std::vector<T>& a, const std::vector<T>& b) {int n = int(a.size()), m = int(b.size());if (!n || !m) return {};using mint = static_modint<mod>;std::vector<mint> a2(n), b2(m);for (int i = 0; i < n; i++) {a2[i] = mint(a[i]);}for (int i = 0; i < m; i++) {b2[i] = mint(b[i]);}auto c2 = convolution(move(a2), move(b2));std::vector<T> c(n + m - 1);for (int i = 0; i < n + m - 1; i++) {c[i] = c2[i].val();}return c;}std::vector<long long> convolution_ll(const std::vector<long long>& a,const std::vector<long long>& b) {int n = int(a.size()), m = int(b.size());if (!n || !m) return {};static constexpr unsigned long long MOD1 = 754974721; // 2^24static constexpr unsigned long long MOD2 = 167772161; // 2^25static constexpr unsigned long long MOD3 = 469762049; // 2^26static constexpr unsigned long long M2M3 = MOD2 * MOD3;static constexpr unsigned long long M1M3 = MOD1 * MOD3;static constexpr unsigned long long M1M2 = MOD1 * MOD2;static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;static constexpr unsigned long long i1 =internal::inv_gcd(MOD2 * MOD3, MOD1).second;static constexpr unsigned long long i2 =internal::inv_gcd(MOD1 * MOD3, MOD2).second;static constexpr unsigned long long i3 =internal::inv_gcd(MOD1 * MOD2, MOD3).second;auto c1 = convolution<MOD1>(a, b);auto c2 = convolution<MOD2>(a, b);auto c3 = convolution<MOD3>(a, b);std::vector<long long> c(n + m - 1);for (int i = 0; i < n + m - 1; i++) {unsigned long long x = 0;x += (c1[i] * i1) % MOD1 * M2M3;x += (c2[i] * i2) % MOD2 * M1M3;x += (c3[i] * i3) % MOD3 * M1M2;long long diff =c1[i] - internal::safe_mod((long long)(x), (long long)(MOD1));if (diff < 0) diff += MOD1;static constexpr unsigned long long offset[5] = {0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3 };x -= offset[diff % 5];c[i] = x;}return c;}} // namespace atcoder#include <algorithm>#include <cassert>#include <vector>namespace atcoder {struct dsu {public:dsu() : _n(0) {}dsu(int n) : _n(n), parent_or_size(n, -1) {}int merge(int a, int b) {assert(0 <= a && a < _n);assert(0 <= b && b < _n);int x = leader(a), y = leader(b);if (x == y) return x;if (-parent_or_size[x] < -parent_or_size[y]) std::swap(x, y);parent_or_size[x] += parent_or_size[y];parent_or_size[y] = x;return x;}bool same(int a, int b) {assert(0 <= a && a < _n);assert(0 <= b && b < _n);return leader(a) == leader(b);}int leader(int a) {assert(0 <= a && a < _n);if (parent_or_size[a] < 0) return a;return parent_or_size[a] = leader(parent_or_size[a]);}int size(int a) {assert(0 <= a && a < _n);return -parent_or_size[leader(a)];}std::vector<std::vector<int>> groups() {std::vector<int> leader_buf(_n), group_size(_n);for (int i = 0; i < _n; i++) {leader_buf[i] = leader(i);group_size[leader_buf[i]]++;}std::vector<std::vector<int>> result(_n);for (int i = 0; i < _n; i++) {result[i].reserve(group_size[i]);}for (int i = 0; i < _n; i++) {result[leader_buf[i]].push_back(i);}result.erase(std::remove_if(result.begin(), result.end(),[&](const std::vector<int>& v) { return v.empty(); }),result.end());return result;}private:int _n;std::vector<int> parent_or_size;};} // namespace atcoder#include <cassert>#include <vector>namespace atcoder {template <class T> struct fenwick_tree {using U = internal::to_unsigned_t<T>;public:fenwick_tree() : _n(0) {}fenwick_tree(int n) : _n(n), data(n) {}void add(int p, T x) {assert(0 <= p && p < _n);p++;while (p <= _n) {data[p - 1] += U(x);p += p & -p;}}T sum(int l, int r) {assert(0 <= l && l <= r && r <= _n);return sum(r) - sum(l);}private:int _n;std::vector<U> data;U sum(int r) {U s = 0;while (r > 0) {s += data[r - 1];r -= r & -r;}return s;}};} // namespace atcoder#include <algorithm>#include <cassert>#include <iostream>#include <vector>namespace atcoder {template <class S,S(*op)(S, S),S(*e)(),class F,S(*mapping)(F, S),F(*composition)(F, F),F(*id)()>struct lazy_segtree {public:lazy_segtree() : lazy_segtree(0) {}lazy_segtree(int n) : lazy_segtree(std::vector<S>(n, e())) {}lazy_segtree(const std::vector<S>& v) : _n(int(v.size())) {log = internal::ceil_pow2(_n);size = 1 << log;d = std::vector<S>(2 * size, e());lz = std::vector<F>(size, id());for (int i = 0; i < _n; i++) d[size + i] = v[i];for (int i = size - 1; i >= 1; i--) {update(i);}}void set(int p, S x) {assert(0 <= p && p < _n);p += size;for (int i = log; i >= 1; i--) push(p >> i);d[p] = x;for (int i = 1; i <= log; i++) update(p >> i);}S get(int p) {assert(0 <= p && p < _n);p += size;for (int i = log; i >= 1; i--) push(p >> i);return d[p];}S prod(int l, int r) {assert(0 <= l && l <= r && r <= _n);if (l == r) return e();l += size;r += size;for (int i = log; i >= 1; i--) {if (((l >> i) << i) != l) push(l >> i);if (((r >> i) << i) != r) push(r >> i);}S sml = e(), smr = e();while (l < r) {if (l & 1) sml = op(sml, d[l++]);if (r & 1) smr = op(d[--r], smr);l >>= 1;r >>= 1;}return op(sml, smr);}S all_prod() { return d[1]; }void apply(int p, F f) {assert(0 <= p && p < _n);p += size;for (int i = log; i >= 1; i--) push(p >> i);d[p] = mapping(f, d[p]);for (int i = 1; i <= log; i++) update(p >> i);}void apply(int l, int r, F f) {assert(0 <= l && l <= r && r <= _n);if (l == r) return;l += size;r += size;for (int i = log; i >= 1; i--) {if (((l >> i) << i) != l) push(l >> i);if (((r >> i) << i) != r) push((r - 1) >> i);}{int l2 = l, r2 = r;while (l < r) {if (l & 1) all_apply(l++, f);if (r & 1) all_apply(--r, f);l >>= 1;r >>= 1;}l = l2;r = r2;}for (int i = 1; i <= log; i++) {if (((l >> i) << i) != l) update(l >> i);if (((r >> i) << i) != r) update((r - 1) >> i);}}template <bool (*g)(S)> int max_right(int l) {return max_right(l, [](S x) { return g(x); });}template <class G> int max_right(int l, G g) {assert(0 <= l && l <= _n);assert(g(e()));if (l == _n) return _n;l += size;for (int i = log; i >= 1; i--) push(l >> i);S sm = e();do {while (l % 2 == 0) l >>= 1;if (!g(op(sm, d[l]))) {while (l < size) {push(l);l = (2 * l);if (g(op(sm, d[l]))) {sm = op(sm, d[l]);l++;}}return l - size;}sm = op(sm, d[l]);l++;} while ((l & -l) != l);return _n;}template <bool (*g)(S)> int min_left(int r) {return min_left(r, [](S x) { return g(x); });}template <class G> int min_left(int r, G g) {assert(0 <= r && r <= _n);assert(g(e()));if (r == 0) return 0;r += size;for (int i = log; i >= 1; i--) push((r - 1) >> i);S sm = e();do {r--;while (r > 1 && (r % 2)) r >>= 1;if (!g(op(d[r], sm))) {while (r < size) {push(r);r = (2 * r + 1);if (g(op(d[r], sm))) {sm = op(d[r], sm);r--;}}return r + 1 - size;}sm = op(d[r], sm);} while ((r & -r) != r);return 0;}private:int _n, size, log;std::vector<S> d;std::vector<F> lz;void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }void all_apply(int k, F f) {d[k] = mapping(f, d[k]);if (k < size) lz[k] = composition(f, lz[k]);}void push(int k) {all_apply(2 * k, lz[k]);all_apply(2 * k + 1, lz[k]);lz[k] = id();}};} // namespace atcoder#include <algorithm>#include <cassert>#include <tuple>#include <vector>namespace atcoder {long long pow_mod(long long x, long long n, int m) {assert(0 <= n && 1 <= m);if (m == 1) return 0;internal::barrett bt((unsigned int)(m));unsigned int r = 1, y = (unsigned int)(internal::safe_mod(x, m));while (n) {if (n & 1) r = bt.mul(r, y);y = bt.mul(y, y);n >>= 1;}return r;}long long inv_mod(long long x, long long m) {assert(1 <= m);auto z = internal::inv_gcd(x, m);assert(z.first == 1);return z.second;}std::pair<long long, long long> crt(const std::vector<long long>& r,const std::vector<long long>& m) {assert(r.size() == m.size());int n = int(r.size());long long r0 = 0, m0 = 1;for (int i = 0; i < n; i++) {assert(1 <= m[i]);long long r1 = internal::safe_mod(r[i], m[i]), m1 = m[i];if (m0 < m1) {std::swap(r0, r1);std::swap(m0, m1);}if (m0 % m1 == 0) {if (r0 % m1 != r1) return { 0, 0 };continue;}long long g, im;std::tie(g, im) = internal::inv_gcd(m0, m1);long long u1 = (m1 / g);if ((r1 - r0) % g) return { 0, 0 };long long x = (r1 - r0) / g % u1 * im % u1;r0 += x * m0;m0 *= u1; // -> lcm(m0, m1)if (r0 < 0) r0 += m0;}return { r0, m0 };}long long floor_sum(long long n, long long m, long long a, long long b) {long long ans = 0;if (a >= m) {ans += (n - 1) * n * (a / m) / 2;a %= m;}if (b >= m) {ans += n * (b / m);b %= m;}long long y_max = (a * n + b) / m, x_max = (y_max * m - b);if (y_max == 0) return ans;ans += (n - (x_max + a - 1) / a) * y_max;ans += floor_sum(y_max, a, m, (a - x_max % a) % a);return ans;}} // namespace atcoder#include <algorithm>#include <vector>namespace atcoder {namespace internal {template <class T> struct simple_queue {std::vector<T> payload;int pos = 0;void reserve(int n) { payload.reserve(n); }int size() const { return int(payload.size()) - pos; }bool empty() const { return pos == int(payload.size()); }void push(const T& t) { payload.push_back(t); }T& front() { return payload[pos]; }void clear() {payload.clear();pos = 0;}void pop() { pos++; }};} // namespace internal} // namespace atcoder#include <cassert>#include <limits>#include <queue>#include <vector>namespace atcoder {template <class Cap> struct mf_graph {public:mf_graph() : _n(0) {}mf_graph(int n) : _n(n), g(n) {}int add_edge(int from, int to, Cap cap) {assert(0 <= from && from < _n);assert(0 <= to && to < _n);assert(0 <= cap);int m = int(pos.size());pos.push_back({ from, int(g[from].size()) });g[from].push_back(_edge{ to, int(g[to].size()), cap });g[to].push_back(_edge{ from, int(g[from].size()) - 1, 0 });return m;}struct edge {int from, to;Cap cap, flow;};edge get_edge(int i) {int m = int(pos.size());assert(0 <= i && i < m);auto _e = g[pos[i].first][pos[i].second];auto _re = g[_e.to][_e.rev];return edge{ pos[i].first, _e.to, _e.cap + _re.cap, _re.cap };}std::vector<edge> edges() {int m = int(pos.size());std::vector<edge> result;for (int i = 0; i < m; i++) {result.push_back(get_edge(i));}return result;}void change_edge(int i, Cap new_cap, Cap new_flow) {int m = int(pos.size());assert(0 <= i && i < m);assert(0 <= new_flow && new_flow <= new_cap);auto& _e = g[pos[i].first][pos[i].second];auto& _re = g[_e.to][_e.rev];_e.cap = new_cap - new_flow;_re.cap = new_flow;}Cap flow(int s, int t) {return flow(s, t, std::numeric_limits<Cap>::max());}Cap flow(int s, int t, Cap flow_limit) {assert(0 <= s && s < _n);assert(0 <= t && t < _n);std::vector<int> level(_n), iter(_n);internal::simple_queue<int> que;auto bfs = [&]() {std::fill(level.begin(), level.end(), -1);level[s] = 0;que.clear();que.push(s);while (!que.empty()) {int v = que.front();que.pop();for (auto e : g[v]) {if (e.cap == 0 || level[e.to] >= 0) continue;level[e.to] = level[v] + 1;if (e.to == t) return;que.push(e.to);}}};auto dfs = [&](auto self, int v, Cap up) {if (v == s) return up;Cap res = 0;int level_v = level[v];for (int& i = iter[v]; i < int(g[v].size()); i++) {_edge& e = g[v][i];if (level_v <= level[e.to] || g[e.to][e.rev].cap == 0) continue;Cap d =self(self, e.to, std::min(up - res, g[e.to][e.rev].cap));if (d <= 0) continue;g[v][i].cap += d;g[e.to][e.rev].cap -= d;res += d;if (res == up) break;}return res;};Cap flow = 0;while (flow < flow_limit) {bfs();if (level[t] == -1) break;std::fill(iter.begin(), iter.end(), 0);while (flow < flow_limit) {Cap f = dfs(dfs, t, flow_limit - flow);if (!f) break;flow += f;}}return flow;}std::vector<bool> min_cut(int s) {std::vector<bool> visited(_n);internal::simple_queue<int> que;que.push(s);while (!que.empty()) {int p = que.front();que.pop();visited[p] = true;for (auto e : g[p]) {if (e.cap && !visited[e.to]) {visited[e.to] = true;que.push(e.to);}}}return visited;}private:int _n;struct _edge {int to, rev;Cap cap;};std::vector<std::pair<int, int>> pos;std::vector<std::vector<_edge>> g;};} // namespace atcoder#include <algorithm>#include <cassert>#include <limits>#include <queue>#include <vector>namespace atcoder {template <class Cap, class Cost> struct mcf_graph {public:mcf_graph() {}mcf_graph(int n) : _n(n), g(n) {}int add_edge(int from, int to, Cap cap, Cost cost) {assert(0 <= from && from < _n);assert(0 <= to && to < _n);int m = int(pos.size());pos.push_back({ from, int(g[from].size()) });g[from].push_back(_edge{ to, int(g[to].size()), cap, cost });g[to].push_back(_edge{ from, int(g[from].size()) - 1, 0, -cost });return m;}struct edge {int from, to;Cap cap, flow;Cost cost;};edge get_edge(int i) {int m = int(pos.size());assert(0 <= i && i < m);auto _e = g[pos[i].first][pos[i].second];auto _re = g[_e.to][_e.rev];return edge{pos[i].first, _e.to, _e.cap + _re.cap, _re.cap, _e.cost,};}std::vector<edge> edges() {int m = int(pos.size());std::vector<edge> result(m);for (int i = 0; i < m; i++) {result[i] = get_edge(i);}return result;}std::pair<Cap, Cost> flow(int s, int t) {return flow(s, t, std::numeric_limits<Cap>::max());}std::pair<Cap, Cost> flow(int s, int t, Cap flow_limit) {return slope(s, t, flow_limit).back();}std::vector<std::pair<Cap, Cost>> slope(int s, int t) {return slope(s, t, std::numeric_limits<Cap>::max());}std::vector<std::pair<Cap, Cost>> slope(int s, int t, Cap flow_limit) {assert(0 <= s && s < _n);assert(0 <= t && t < _n);assert(s != t);std::vector<Cost> dual(_n, 0), dist(_n);std::vector<int> pv(_n), pe(_n);std::vector<bool> vis(_n);auto dual_ref = [&]() {std::fill(dist.begin(), dist.end(),std::numeric_limits<Cost>::max());std::fill(pv.begin(), pv.end(), -1);std::fill(pe.begin(), pe.end(), -1);std::fill(vis.begin(), vis.end(), false);struct Q {Cost key;int to;bool operator<(Q r) const { return key > r.key; }};std::priority_queue<Q> que;dist[s] = 0;que.push(Q{ 0, s });while (!que.empty()) {int v = que.top().to;que.pop();if (vis[v]) continue;vis[v] = true;if (v == t) break;for (int i = 0; i < int(g[v].size()); i++) {auto e = g[v][i];if (vis[e.to] || !e.cap) continue;Cost cost = e.cost - dual[e.to] + dual[v];if (dist[e.to] - dist[v] > cost) {dist[e.to] = dist[v] + cost;pv[e.to] = v;pe[e.to] = i;que.push(Q{ dist[e.to], e.to });}}}if (!vis[t]) {return false;}for (int v = 0; v < _n; v++) {if (!vis[v]) continue;dual[v] -= dist[t] - dist[v];}return true;};Cap flow = 0;Cost cost = 0, prev_cost = -1;std::vector<std::pair<Cap, Cost>> result;result.push_back({ flow, cost });while (flow < flow_limit) {if (!dual_ref()) break;Cap c = flow_limit - flow;for (int v = t; v != s; v = pv[v]) {c = std::min(c, g[pv[v]][pe[v]].cap);}for (int v = t; v != s; v = pv[v]) {auto& e = g[pv[v]][pe[v]];e.cap -= c;g[v][e.rev].cap += c;}Cost d = -dual[s];flow += c;cost += c * d;if (prev_cost == d) {result.pop_back();}result.push_back({ flow, cost });prev_cost = cost;}return result;}private:int _n;struct _edge {int to, rev;Cap cap;Cost cost;};std::vector<std::pair<int, int>> pos;std::vector<std::vector<_edge>> g;};} // namespace atcoder#include <algorithm>#include <algorithm>#include <utility>#include <vector>namespace atcoder {namespace internal {template <class E> struct csr {std::vector<int> start;std::vector<E> elist;csr(int n, const std::vector<std::pair<int, E>>& edges): start(n + 1), elist(edges.size()) {for (auto e : edges) {start[e.first + 1]++;}for (int i = 1; i <= n; i++) {start[i] += start[i - 1];}auto counter = start;for (auto e : edges) {elist[counter[e.first]++] = e.second;}}};struct scc_graph {public:scc_graph(int n) : _n(n) {}int num_vertices() { return _n; }void add_edge(int from, int to) { edges.push_back({ from, {to} }); }std::pair<int, std::vector<int>> scc_ids() {auto g = csr<edge>(_n, edges);int now_ord = 0, group_num = 0;std::vector<int> visited, low(_n), ord(_n, -1), ids(_n);visited.reserve(_n);auto dfs = [&](auto self, int v) -> void {low[v] = ord[v] = now_ord++;visited.push_back(v);for (int i = g.start[v]; i < g.start[v + 1]; i++) {auto to = g.elist[i].to;if (ord[to] == -1) {self(self, to);low[v] = std::min(low[v], low[to]);}else {low[v] = std::min(low[v], ord[to]);}}if (low[v] == ord[v]) {while (true) {int u = visited.back();visited.pop_back();ord[u] = _n;ids[u] = group_num;if (u == v) break;}group_num++;}};for (int i = 0; i < _n; i++) {if (ord[i] == -1) dfs(dfs, i);}for (auto& x : ids) {x = group_num - 1 - x;}return { group_num, ids };}std::vector<std::vector<int>> scc() {auto ids = scc_ids();int group_num = ids.first;std::vector<int> counts(group_num);for (auto x : ids.second) counts[x]++;std::vector<std::vector<int>> groups(ids.first);for (int i = 0; i < group_num; i++) {groups[i].reserve(counts[i]);}for (int i = 0; i < _n; i++) {groups[ids.second[i]].push_back(i);}return groups;}private:int _n;struct edge {int to;};std::vector<std::pair<int, edge>> edges;};} // namespace internal} // namespace atcoder#include <cassert>#include <vector>namespace atcoder {struct scc_graph {public:scc_graph() : internal(0) {}scc_graph(int n) : internal(n) {}void add_edge(int from, int to) {int n = internal.num_vertices();assert(0 <= from && from < n);assert(0 <= to && to < n);internal.add_edge(from, to);}std::vector<std::vector<int>> scc() { return internal.scc(); }private:internal::scc_graph internal;};} // namespace atcoder#include <algorithm>#include <cassert>#include <vector>namespace atcoder {template <class S, S(*op)(S, S), S(*e)()> struct segtree {public:segtree() : segtree(0) {}segtree(int n) : segtree(std::vector<S>(n, e())) {}segtree(const std::vector<S>& v) : _n(int(v.size())) {log = internal::ceil_pow2(_n);size = 1 << log;d = std::vector<S>(2 * size, e());for (int i = 0; i < _n; i++) d[size + i] = v[i];for (int i = size - 1; i >= 1; i--) {update(i);}}void set(int p, S x) {assert(0 <= p && p < _n);p += size;d[p] = x;for (int i = 1; i <= log; i++) update(p >> i);}S get(int p) {assert(0 <= p && p < _n);return d[p + size];}S prod(int l, int r) {assert(0 <= l && l <= r && r <= _n);S sml = e(), smr = e();l += size;r += size;while (l < r) {if (l & 1) sml = op(sml, d[l++]);if (r & 1) smr = op(d[--r], smr);l >>= 1;r >>= 1;}return op(sml, smr);}S all_prod() { return d[1]; }template <bool (*f)(S)> int max_right(int l) {return max_right(l, [](S x) { return f(x); });}template <class F> int max_right(int l, F f) {assert(0 <= l && l <= _n);assert(f(e()));if (l == _n) return _n;l += size;S sm = e();do {while (l % 2 == 0) l >>= 1;if (!f(op(sm, d[l]))) {while (l < size) {l = (2 * l);if (f(op(sm, d[l]))) {sm = op(sm, d[l]);l++;}}return l - size;}sm = op(sm, d[l]);l++;} while ((l & -l) != l);return _n;}template <bool (*f)(S)> int min_left(int r) {return min_left(r, [](S x) { return f(x); });}template <class F> int min_left(int r, F f) {assert(0 <= r && r <= _n);assert(f(e()));if (r == 0) return 0;r += size;S sm = e();do {r--;while (r > 1 && (r % 2)) r >>= 1;if (!f(op(d[r], sm))) {while (r < size) {r = (2 * r + 1);if (f(op(d[r], sm))) {sm = op(d[r], sm);r--;}}return r + 1 - size;}sm = op(d[r], sm);} while ((r & -r) != r);return 0;}private:int _n, size, log;std::vector<S> d;void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }};} // namespace atcoder#include <algorithm>#include <cassert>#include <numeric>#include <string>#include <vector>namespace atcoder {namespace internal {std::vector<int> sa_naive(const std::vector<int>& s) {int n = int(s.size());std::vector<int> sa(n);std::iota(sa.begin(), sa.end(), 0);std::sort(sa.begin(), sa.end(), [&](int l, int r) {if (l == r) return false;while (l < n && r < n) {if (s[l] != s[r]) return s[l] < s[r];l++;r++;}return l == n;});return sa;}std::vector<int> sa_doubling(const std::vector<int>& s) {int n = int(s.size());std::vector<int> sa(n), rnk = s, tmp(n);std::iota(sa.begin(), sa.end(), 0);for (int k = 1; k < n; k *= 2) {auto cmp = [&](int x, int y) {if (rnk[x] != rnk[y]) return rnk[x] < rnk[y];int rx = x + k < n ? rnk[x + k] : -1;int ry = y + k < n ? rnk[y + k] : -1;return rx < ry;};std::sort(sa.begin(), sa.end(), cmp);tmp[sa[0]] = 0;for (int i = 1; i < n; i++) {tmp[sa[i]] = tmp[sa[i - 1]] + (cmp(sa[i - 1], sa[i]) ? 1 : 0);}std::swap(tmp, rnk);}return sa;}template <int THRESHOLD_NAIVE = 10, int THRESHOLD_DOUBLING = 40>std::vector<int> sa_is(const std::vector<int>& s, int upper) {int n = int(s.size());if (n == 0) return {};if (n == 1) return { 0 };if (n == 2) {if (s[0] < s[1]) {return { 0, 1 };}else {return { 1, 0 };}}if (n < THRESHOLD_NAIVE) {return sa_naive(s);}if (n < THRESHOLD_DOUBLING) {return sa_doubling(s);}std::vector<int> sa(n);std::vector<bool> ls(n);for (int i = n - 2; i >= 0; i--) {ls[i] = (s[i] == s[i + 1]) ? ls[i + 1] : (s[i] < s[i + 1]);}std::vector<int> sum_l(upper + 1), sum_s(upper + 1);for (int i = 0; i < n; i++) {if (!ls[i]) {sum_s[s[i]]++;}else {sum_l[s[i] + 1]++;}}for (int i = 0; i <= upper; i++) {sum_s[i] += sum_l[i];if (i < upper) sum_l[i + 1] += sum_s[i];}auto induce = [&](const std::vector<int>& lms) {std::fill(sa.begin(), sa.end(), -1);std::vector<int> buf(upper + 1);std::copy(sum_s.begin(), sum_s.end(), buf.begin());for (auto d : lms) {if (d == n) continue;sa[buf[s[d]]++] = d;}std::copy(sum_l.begin(), sum_l.end(), buf.begin());sa[buf[s[n - 1]]++] = n - 1;for (int i = 0; i < n; i++) {int v = sa[i];if (v >= 1 && !ls[v - 1]) {sa[buf[s[v - 1]]++] = v - 1;}}std::copy(sum_l.begin(), sum_l.end(), buf.begin());for (int i = n - 1; i >= 0; i--) {int v = sa[i];if (v >= 1 && ls[v - 1]) {sa[--buf[s[v - 1] + 1]] = v - 1;}}};std::vector<int> lms_map(n + 1, -1);int m = 0;for (int i = 1; i < n; i++) {if (!ls[i - 1] && ls[i]) {lms_map[i] = m++;}}std::vector<int> lms;lms.reserve(m);for (int i = 1; i < n; i++) {if (!ls[i - 1] && ls[i]) {lms.push_back(i);}}induce(lms);if (m) {std::vector<int> sorted_lms;sorted_lms.reserve(m);for (int v : sa) {if (lms_map[v] != -1) sorted_lms.push_back(v);}std::vector<int> rec_s(m);int rec_upper = 0;rec_s[lms_map[sorted_lms[0]]] = 0;for (int i = 1; i < m; i++) {int l = sorted_lms[i - 1], r = sorted_lms[i];int end_l = (lms_map[l] + 1 < m) ? lms[lms_map[l] + 1] : n;int end_r = (lms_map[r] + 1 < m) ? lms[lms_map[r] + 1] : n;bool same = true;if (end_l - l != end_r - r) {same = false;}else {while (l < end_l) {if (s[l] != s[r]) {break;}l++;r++;}if (l == n || s[l] != s[r]) same = false;}if (!same) rec_upper++;rec_s[lms_map[sorted_lms[i]]] = rec_upper;}auto rec_sa =sa_is<THRESHOLD_NAIVE, THRESHOLD_DOUBLING>(rec_s, rec_upper);for (int i = 0; i < m; i++) {sorted_lms[i] = lms[rec_sa[i]];}induce(sorted_lms);}return sa;}} // namespace internalstd::vector<int> suffix_array(const std::vector<int>& s, int upper) {assert(0 <= upper);for (int d : s) {assert(0 <= d && d <= upper);}auto sa = internal::sa_is(s, upper);return sa;}template <class T> std::vector<int> suffix_array(const std::vector<T>& s) {int n = int(s.size());std::vector<int> idx(n);iota(idx.begin(), idx.end(), 0);sort(idx.begin(), idx.end(), [&](int l, int r) { return s[l] < s[r]; });std::vector<int> s2(n);int now = 0;for (int i = 0; i < n; i++) {if (i && s[idx[i - 1]] != s[idx[i]]) now++;s2[idx[i]] = now;}return internal::sa_is(s2, now);}std::vector<int> suffix_array(const std::string& s) {int n = int(s.size());std::vector<int> s2(n);for (int i = 0; i < n; i++) {s2[i] = s[i];}return internal::sa_is(s2, 255);}template <class T>std::vector<int> lcp_array(const std::vector<T>& s,const std::vector<int>& sa) {int n = int(s.size());assert(n >= 1);std::vector<int> rnk(n);for (int i = 0; i < n; i++) {rnk[sa[i]] = i;}std::vector<int> lcp(n - 1);int h = 0;for (int i = 0; i < n; i++) {if (h > 0) h--;if (rnk[i] == 0) continue;int j = sa[rnk[i] - 1];for (; j + h < n && i + h < n; h++) {if (s[j + h] != s[i + h]) break;}lcp[rnk[i] - 1] = h;}return lcp;}std::vector<int> lcp_array(const std::string& s, const std::vector<int>& sa) {int n = int(s.size());std::vector<int> s2(n);for (int i = 0; i < n; i++) {s2[i] = s[i];}return lcp_array(s2, sa);}template <class T> std::vector<int> z_algorithm(const std::vector<T>& s) {int n = int(s.size());if (n == 0) return {};std::vector<int> z(n);z[0] = 0;for (int i = 1, j = 0; i < n; i++) {int& k = z[i];k = (j + z[j] <= i) ? 0 : std::min(j + z[j] - i, z[i - j]);while (i + k < n && s[k] == s[i + k]) k++;if (j + z[j] < i + z[i]) j = i;}z[0] = n;return z;}std::vector<int> z_algorithm(const std::string& s) {int n = int(s.size());std::vector<int> s2(n);for (int i = 0; i < n; i++) {s2[i] = s[i];}return z_algorithm(s2);}} // namespace atcoder#include <cassert>#include <vector>namespace atcoder {struct two_sat {public:two_sat() : _n(0), scc(0) {}two_sat(int n) : _n(n), _answer(n), scc(2 * n) {}void add_clause(int i, bool f, int j, bool g) {assert(0 <= i && i < _n);assert(0 <= j && j < _n);scc.add_edge(2 * i + (f ? 0 : 1), 2 * j + (g ? 1 : 0));scc.add_edge(2 * j + (g ? 0 : 1), 2 * i + (f ? 1 : 0));}bool satisfiable() {auto id = scc.scc_ids().second;for (int i = 0; i < _n; i++) {if (id[2 * i] == id[2 * i + 1]) return false;_answer[i] = id[2 * i] < id[2 * i + 1];}return true;}std::vector<bool> answer() { return _answer; }private:int _n;std::vector<bool> _answer;internal::scc_graph scc;};} // namespace atcoder/*end of AtCoder STL*/#define int llusing namespace std;using namespace atcoder;typedef string::const_iterator State;#define eps 1e-8L#define MAX_MOD 1000000007LL#define GYAKU 500000004LL#define MOD 998244353LL#define pb push_back#define mp make_pairtypedef long long ll;typedef long double ld;#define REP(a,b) for(long long (a) = 0;(a) < (b);++(a))#define ALL(x) (x).begin(),(x).end()unsigned long xor128() {static unsigned long x = 123456789, y = 362436069, z = 521288629, w = 88675123;unsigned long t = (x ^ (x << 11));x = y; y = z; z = w;return (w = (w ^ (w >> 19)) ^ (t ^ (t >> 8)));};typedef complex<long double> Point;typedef pair<complex<long double>, complex<long double>> Line;typedef struct Circle {complex<long double> center;long double r;}Circle;long double dot(Point a, Point b) {return (a.real() * b.real() + a.imag() * b.imag());}long double cross(Point a, Point b) {return (a.real() * b.imag() - a.imag() * b.real());}long double Dist_Line_Point(Line a, Point b) {if (dot(a.second - a.first, b - a.first) < eps) return abs(b - a.first);if (dot(a.first - a.second, b - a.second) < eps) return abs(b - a.second);return abs(cross(a.second - a.first, b - a.first)) / abs(a.second - a.first);}int is_intersected_ls(Line a, Line b) {return (cross(a.second - a.first, b.first - a.first) * cross(a.second - a.first, b.second - a.first) < eps) &&(cross(b.second - b.first, a.first - b.first) * cross(b.second - b.first, a.second - b.first) < eps);}Point intersection_l(Line a, Line b) {Point da = a.second - a.first;Point db = b.second - b.first;return a.first + da * cross(db, b.first - a.first) / cross(db, da);}long double Dist_Line_Line(Line a, Line b) {if (is_intersected_ls(a, b) == 1) {return 0;}return min({ Dist_Line_Point(a,b.first), Dist_Line_Point(a,b.second),Dist_Line_Point(b,a.first),Dist_Line_Point(b,a.second) });}pair<Point, Point> intersection_Circle_Circle(Circle a, Circle b) {long double dist = abs(a.center - b.center);assert(dist <= eps + a.r + b.r);assert(dist + eps >= abs(a.r - b.r));Point target = b.center - a.center;long double pointer = target.real() * target.real() + target.imag() * target.imag();long double aa = pointer + a.r * a.r - b.r * b.r;aa /= 2.0L;Point l{ (aa * target.real() + target.imag() * sqrt(pointer * a.r * a.r - aa * aa)) / pointer,(aa * target.imag() - target.real() * sqrt(pointer * a.r * a.r - aa * aa)) / pointer };Point r{ (aa * target.real() - target.imag() * sqrt(pointer * a.r * a.r - aa * aa)) / pointer,(aa * target.imag() + target.real() * sqrt(pointer * a.r * a.r - aa * aa)) / pointer };r = r + a.center;l = l + a.center;return mp(l, r);}ll gcd(ll a, ll b) {if (b == 0) return a;return gcd(b, a % b);}template<typename A>A pows(A val, ll b) {assert(b >= 1);A ans = val;b--;while (b) {if (b % 2) {ans *= val;}val *= val;b /= 2LL;}return ans;}template<typename A>class Compressor {public:bool is_zipped = false;map<A, ll> zipper;map<ll, A> unzipper;queue<A> fetcher;Compressor() {is_zipped = false;zipper.clear();unzipper.clear();}void add(A now) {assert(is_zipped == false);zipper[now] = 1;fetcher.push(now);}void exec() {assert(is_zipped == false);int cnt = 0;for (auto i = zipper.begin(); i != zipper.end(); ++i) {i->second = cnt;unzipper[cnt] = i->first;cnt++;}is_zipped = true;}ll fetch() {assert(is_zipped == true);A hoge = fetcher.front();fetcher.pop();return zipper[hoge];}ll zip(A now) {assert(is_zipped == true);assert(zipper.find(now) != zipper.end());return zipper[now];}A unzip(ll a) {assert(is_zipped == true);assert(a < unzipper.size());return unzipper[a];}ll next(A now) {auto x = zipper.upper_bound(now);if (x == zipper.end()) return zipper.size();return (ll)((*x).second);}ll back(A now) {auto x = zipper.lower_bound(now);if (x == zipper.begin()) return -1;x--;return (ll)((*x).second);}};template<typename A>class Matrix {public:vector<vector<A>> data;Matrix(vector<vector<A>> a) :data(a) {}Matrix operator + (const Matrix obj) {vector<vector<A>> ans;assert(obj.data.size() == this->data.size());assert(obj.data[0].size() == this->data[0].size());REP(i, obj.data.size()) {ans.push_back(vector<A>());REP(q, obj.data[i].size()) {A hoge = obj.data[i][q] + (this->data[i][q]);ans.back().push_back(hoge);}}return Matrix(ans);}Matrix operator - (const Matrix obj) {vector<vector<A>> ans;assert(obj.data.size() == this->data.size());assert(obj.data[0].size() == this->data[0].size());REP(i, obj.data.size()) {ans.push_back(vector<A>());REP(q, obj.data[i].size()) {A hoge = this->data[i][q] - obj.data[i][q];ans.back().push_back(hoge);}}return Matrix(ans);}Matrix operator * (const Matrix obj) {vector<vector<A>> ans;assert(obj.data.size() == this->data[0].size());REP(i, this -> data.size()) {ans.push_back(vector<A>());REP(q, obj.data[0].size()) {A hoge = ((this->data[i][0]) * (obj.data[0][q]));for (int t = 1; t < obj.data.size(); ++t) {hoge += ((this->data[i][t]) * obj.data[t][q]);}ans.back().push_back(hoge);}}return Matrix(ans);}Matrix& operator *= (const Matrix obj) {*this = (*this * obj);return *this;}Matrix& operator += (const Matrix obj) {*this = (*this + obj);return *this;}Matrix& operator -= (const Matrix obj) {*this = (*this - obj);return *this;}};struct Fraction {ll a;ll b;Fraction() :a(0LL), b(1LL) {}Fraction(ll c, ll d) {int hoge = gcd(llabs(c), llabs(d));if (hoge != 0) {c /= hoge;d /= hoge;if (d < 0 or (d == 0 and c < 0)) {d *= -1;c *= -1;}}a = c;b = d;}bool operator <(Fraction rhs) const {if (a < 0 and rhs.a > 0) return 1;if (a > 0 and rhs.a < 0) return 0;return a * rhs.b < rhs.a* b;}bool operator ==(Fraction rhs) const {return a == rhs.a and b == rhs.b;}};class Dice {public:vector<ll> vertexs;Dice(vector<ll> init) :vertexs(init) {}void RtoL() {for (int q = 1; q < 4; ++q) {swap(vertexs[q], vertexs[q + 1]);}}void LtoR() {for (int q = 3; q >= 1; --q) {swap(vertexs[q], vertexs[q + 1]);}}void UtoD() {swap(vertexs[5], vertexs[4]);swap(vertexs[2], vertexs[5]);swap(vertexs[0], vertexs[2]);}void DtoU() {swap(vertexs[0], vertexs[2]);swap(vertexs[2], vertexs[5]);swap(vertexs[5], vertexs[4]);}bool ReachAble(Dice now) {set<Dice> hoge;queue<Dice> next;next.push(now);hoge.insert(now);while (next.empty() == false) {Dice seeing = next.front();next.pop();if (seeing == *this) return true;seeing.RtoL();if (hoge.count(seeing) == 0) {hoge.insert(seeing);next.push(seeing);}seeing.LtoR();seeing.LtoR();if (hoge.count(seeing) == 0) {hoge.insert(seeing);next.push(seeing);}seeing.RtoL();seeing.UtoD();if (hoge.count(seeing) == 0) {hoge.insert(seeing);next.push(seeing);}seeing.DtoU();seeing.DtoU();if (hoge.count(seeing) == 0) {hoge.insert(seeing);next.push(seeing);}}return false;}bool operator ==(const Dice& a) {for (int q = 0; q < 6; ++q) {if (a.vertexs[q] != (*this).vertexs[q]) {return false;}}return true;}bool operator <(const Dice& a) const {return (*this).vertexs < a.vertexs;}};pair<Dice, Dice> TwoDimDice(int center, int up) {int target = 1;while (true) {if (center != target && 7 - center != target && up != target && 7 - up != target) {break;}target++;}return mp(Dice(vector<ll>{up, target, center, 7 - target, 7 - center, 7 - up}), Dice(vector<ll>{up, 7 - target, center, target, 7 - center, 7 -up}));}tuple<Dice, Dice, Dice, Dice> OneDimDice(int center) {int bo = min(center, 7 - center);pair<int, int> goa;if (bo == 1) {goa = mp(2, 3);}else if (bo == 2) {goa = mp(1, 3);}else if (bo == 3) {goa = mp(1, 2);}tuple<Dice, Dice, Dice, Dice> now = make_tuple(Dice(vector<ll>{goa.first, goa.second, center, 7 - goa.second, 7 - center, 7 - goa.first}),Dice(vector<ll>{goa.first, 7 - goa.second, center, goa.second, 7 - center, 7 - goa.first}),Dice(vector<ll>{7 - goa.first, goa.second, center, 7 - goa.second, 7 - center, goa.first}),Dice(vector<ll>{7 - goa.first, 7 - goa.second, center, goa.second, 7 - center, goa.first}));return now;}class HLDecomposition {public:vector<vector<int>> vertexs;vector<int> depth;vector<int> backs;vector<int> connections;vector<int> zip, unzip;HLDecomposition(int n) {vertexs = vector<vector<int>>(n, vector<int>());depth = vector<int>(n);zip = vector<int>(n);unzip = zip;}void add_edge(int a, int b) {vertexs[a].push_back(b);vertexs[b].push_back(a);}int depth_dfs(int now, int back) {depth[now] = 0;for (auto x : vertexs[now]) {if (x == back) continue;depth[now] = max(depth[now], 1 + depth_dfs(x, now));}return depth[now];}void dfs(int now, int backing) {zip[now] = backs.size();unzip[backs.size()] = now;backs.push_back(backing);int now_max = -1;int itr = -1;for (auto x : vertexs[now]) {if (depth[x] > depth[now]) continue;if (now_max < depth[x]) {now_max = depth[x];itr = x;}}if (itr == -1) return;connections.push_back(connections.back());dfs(itr, backing);for (auto x : vertexs[now]) {if (depth[x] > depth[now]) continue;if (x == itr) continue;connections.push_back(zip[now]);dfs(x, backs.size());}return;}void build() {depth_dfs(0, -1);connections.push_back(-1);dfs(0, -1);}vector<pair<int, int>> query(int a, int b) {a = zip[a];b = zip[b];vector<pair<int, int>> ans;while (backs[a] != backs[b]) {if (a < b) swap(a, b);ans.push_back(mp(backs[a], a + 1));a = connections[a];}if (a > b) swap(a, b);ans.push_back(mp(a, b + 1));return ans;}int lca(int a, int b) {a = zip[a];b = zip[b];while (backs[a] != backs[b]) {if (a < b) swap(a, b);a = connections[a];}return unzip[min(a, b)];}};void init() {iostream::sync_with_stdio(false);cout << fixed << setprecision(20);}#define int llvoid solve() {int n;cin >> n;REP(i, n) {int d;cin >> d;if (d == 1) {cout << 10 << endl;continue;}cout << 9;REP(q, d - 1) cout << 0;cout << endl;}}#undef intint main() {init();int t = 1;//cin >> t;REP(i, t)solve();}