#include <algorithm> 
#include <bitset> 
#include <cassert>
#include <cctype>
#include <cerrno>
#include <cfloat>
#include <ciso646>
#include <climits>
#include <clocale>
#include <cmath>
#include <complex>
#include <csetjmp>
#include <csignal>
#include <cstdarg>
#include <cstddef>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <cwchar>
#include <cwctype>
#include <deque>
#include <exception>
#include <fstream> 
#include <functional> 
#include <iomanip> 
#include <ios> 
#include <iosfwd>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits> 
#include <list> 
#include <locale> 
#include <map>
#include <memory>
#include <new>
#include <numeric> 
#include <ostream>
#include <queue> 
#include <set> 
#include <sstream>
#include <stack>
#include <stdexcept>
#include <streambuf>
#include <string>
#include <strstream> 
#include <typeinfo>
#include <utility>
#include <valarray>
#include <vector>

#if __cplusplus >= 201103
#include <array>
#if __has_include(<atomic>)
#include <atomic>
#endif
#include <chrono>
#if __has_include(<codecvt>)
#include <codecvt>
#endif
#include <condition_variable>
#include <forward_list>
#if __has_include(<future>)
#include <future>
#endif
#include <initializer_list>
#include <mutex>
#include <random>
#include <ratio>
#include <regex>
#if __has_include(<scoped_allocator>)
#include <scoped_allocator>
#endif
#include <system_error>
#include <thread>
#include <tuple>
#include <type_traits>
#if __has_include(<typeindex>)
#include <typeindex>
#endif
#include <unordered_map>
#include <unordered_set>
#endif