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#include <cstring>
#include <cstdio>
#include <cstdlib>
#include <climits>
#include <cmath>

#include <string>
#include <iostream>

#include <algorithm>
#include <set>
#include <map>
#include <vector>

using namespace std;

#define DEBUG false
#define MAXV 500010
#define LL long long
//for loops

#define rep(i,s,n) for(LL (i)=(s);(i)<(LL)(n);(i)++)
#define repr(i,s,n) for(LL (i)=(s);(i)>(LL)(n);(i)--)
#define snuke(c,itr) for(__typeof((c).begin()) itr=(c).begin();itr!=(c).end();itr++)

//vector
#define vl vector<LL>
#define vi vector<int>
#define pb push_back
//pair
#define pll pair<LL,LL> 
#define pii pair<int,int> 
#define fir first
#define sec second


int main(){		
  return 0;
}