include <bits/stdc++.h>

using namespace std;

define FOR(i,a,b) for(int i=(a),b=(b); i<=b; i++)

define FORD(i,a,b) for(int i=(a),b=(b); i>=b; i--)

define REP(i,a) for(int i=0,a=(a); i<a; i++)

define EACH(it,a) for(__typeof(a.begin()) it = a.begin(); it != a.end(); ++it)

define DEBUG(x) { cout << #x << " = "; cout << (x) << endl; }

define PR(a,n) { cout << #a << " = "; FOR(,1,n) cout << a[] << ' '; cout << endl; }

define PR0(a,n) { cout << #a << " = "; REP(,n) cout << a[] << ' '; cout << endl; }

define sqr(x) ((x) * (x))

int t = 1;

void init(); void solve();

int main() { ios::syncwithstdio(0); cin.tie(0); init(); while(t--) solve(); return 0; }