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#include "hack/fastio.hpp"
#pragma once
#include <cstdint>
#include <cstdio>
#include <string>
#include <type_traits>
template <class Char, std::enable_if_t<std::is_same_v<Char, char>, int> = 0>
inline Char in() { return getchar_unlocked(); }
template <class String, std::enable_if_t<std::is_same_v<String, std::string>, int> = 0>
inline std::string in() {
char c; do { c = getchar_unlocked(); } while (isspace(c));
std::string s;
do { s.push_back(c); } while (not isspace(c = getchar_unlocked()));
return s;
}
template <class Integer, std::enable_if_t<std::is_integral_v<Integer> and not std::is_same_v<Integer, char>, int> = 0>
inline Integer in() {
char c; do { c = getchar_unlocked(); } while (isspace(c));
if (std::is_signed<Integer>::value and c == '-') return -in<Integer>();
Integer n = 0;
do { n = n * 10 + c - '0'; } while (not isspace(c = getchar_unlocked()));
return n;
}
template <class Char, std::enable_if_t<std::is_same_v<Char, char>, int> = 0>
inline void out(char c) { putchar_unlocked(c); }
template <class String, std::enable_if_t<std::is_same_v<String, std::string>, int> = 0>
inline void out(const std::string & s) { for (char c : s) putchar_unlocked(c); }
template <class Integer, std::enable_if_t<std::is_integral_v<Integer>, int> = 0>
inline void out(Integer n) {
char s[20];
int i = 0;
if (std::is_signed<Integer>::value and n < 0) { putchar_unlocked('-'); n *= -1; }
do { s[i ++] = n % 10; n /= 10; } while (n);
while (i) putchar_unlocked(s[-- i] + '0');
}
#line 2 "hack/fastio.hpp"
#include <cstdint>
#include <cstdio>
#include <string>
#include <type_traits>
template <class Char, std::enable_if_t<std::is_same_v<Char, char>, int> = 0>
inline Char in() { return getchar_unlocked(); }
template <class String, std::enable_if_t<std::is_same_v<String, std::string>, int> = 0>
inline std::string in() {
char c; do { c = getchar_unlocked(); } while (isspace(c));
std::string s;
do { s.push_back(c); } while (not isspace(c = getchar_unlocked()));
return s;
}
template <class Integer, std::enable_if_t<std::is_integral_v<Integer> and not std::is_same_v<Integer, char>, int> = 0>
inline Integer in() {
char c; do { c = getchar_unlocked(); } while (isspace(c));
if (std::is_signed<Integer>::value and c == '-') return -in<Integer>();
Integer n = 0;
do { n = n * 10 + c - '0'; } while (not isspace(c = getchar_unlocked()));
return n;
}
template <class Char, std::enable_if_t<std::is_same_v<Char, char>, int> = 0>
inline void out(char c) { putchar_unlocked(c); }
template <class String, std::enable_if_t<std::is_same_v<String, std::string>, int> = 0>
inline void out(const std::string & s) { for (char c : s) putchar_unlocked(c); }
template <class Integer, std::enable_if_t<std::is_integral_v<Integer>, int> = 0>
inline void out(Integer n) {
char s[20];
int i = 0;
if (std::is_signed<Integer>::value and n < 0) { putchar_unlocked('-'); n *= -1; }
do { s[i ++] = n % 10; n /= 10; } while (n);
while (i) putchar_unlocked(s[-- i] + '0');
}