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#include <sstream>
#include <string>
#include <vector>
#include <map>
#include <list>
#include <deque>
#include <algorithm>
using namespace std;

typedef vector <int> VI;
typedef vector <string> VS;

#define INF (1 << 31)

#define FOZ(i, n) for(int i = 0; i < n; i++)
#define FOV(i, v) for(int i = 0; i < v.size; i++)
#define FOREACH(it, v) for(typeof(v.begin()) it = v.begin(); it != v.end(); it++)