#include <cassert>
#include <cstdio>
#include <cstdlib>
#include <ctime>
#include <cstring>
#include <cstdarg>
#include <cmath>
#include <vector>
#include <map>
#include <string>
#include <set>
#include <list>
#include <deque>
#include <queue>
#include <bitset>
#include <algorithm>
#include <functional>
#include <limits>
#include <fstream>
#include <iosfwd>
#include <sstream>
#include <sys/types.h>
#include <sys/stat.h>
#include <ext/hash_map>
#include <ext/hash_set>