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#include "template/constant.hpp"
#ifndef KK2_TEMPLATE_CONSTANT_HPP
#define KK2_TEMPLATE_CONSTANT_HPP 1
#include "type_alias.hpp"
template <class T> constexpr T infty = 0;
template <> constexpr int infty<int> = (1 << 30) - 123;
template <> constexpr i64 infty<i64> = (1ll << 62) - (1ll << 31);
template <> constexpr i128 infty<i128> = (i128(1) << 126) - (i128(1) << 63);
template <> constexpr u32 infty<u32> = infty<int>;
template <> constexpr u64 infty<u64> = infty<i64>;
template <> constexpr u128 infty<u128> = infty<i128>;
template <> constexpr double infty<double> = infty<i64>;
template <> constexpr long double infty<long double> = infty<i64>;
constexpr int mod = 998244353;
constexpr int modu = 1e9 + 7;
constexpr long double PI = 3.14159265358979323846;
#endif // KK2_TEMPLATE_CONSTANT_HPP
#line 1 "template/constant.hpp"
#line 1 "template/type_alias.hpp"
#include <functional>
#include <queue>
#include <utility>
#include <vector>
using u32 = unsigned int;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
using pi = std::pair<int, int>;
using pl = std::pair<i64, i64>;
using pil = std::pair<int, i64>;
using pli = std::pair<i64, int>;
template <class T> using vc = std::vector<T>;
template <class T> using vvc = std::vector<vc<T>>;
template <class T> using vvvc = std::vector<vvc<T>>;
template <class T> using vvvvc = std::vector<vvvc<T>>;
template <class T> using pq = std::priority_queue<T>;
template <class T> using pqi = std::priority_queue<T, std::vector<T>, std::greater<T>>;
#line 5 "template/constant.hpp"
template <class T> constexpr T infty = 0;
template <> constexpr int infty<int> = (1 << 30) - 123;
template <> constexpr i64 infty<i64> = (1ll << 62) - (1ll << 31);
template <> constexpr i128 infty<i128> = (i128(1) << 126) - (i128(1) << 63);
template <> constexpr u32 infty<u32> = infty<int>;
template <> constexpr u64 infty<u64> = infty<i64>;
template <> constexpr u128 infty<u128> = infty<i128>;
template <> constexpr double infty<double> = infty<i64>;
template <> constexpr long double infty<long double> = infty<i64>;
constexpr int mod = 998244353;
constexpr int modu = 1e9 + 7;
constexpr long double PI = 3.14159265358979323846;