#include       <set>
#include       <map>
#include      <list>
#include     <cmath>
#include     <queue>
#include     <stack>
#include    <string>
#include    <cstdio>
#include    <vector>
#include   <cstring>
#include   <cstdlib>
#include   <sstream>
#include  <iostream> 
#include <algorithm>
using namespace std;
#define MAX 10005
#define INF 0x3f3f3f3f
typedef pair<int,int> pii;
typedef pair<string,int> psi;
typedef long long ll;