#include "bits/stdc++.h" using namespace std; typedef long long ll; typedef unsigned long long ull; typedef vector veci; typedef vector vecs; template using Hash=unordered_map; #define REP(i, a, n) for(ll i = a; i < (ll)n; i++) #define RREP(i, a, n) for(ll i = n-1; i >= a; i--) #define rep(i, n) REP(i, 0, n) #define rrep(i, n) RREP(i, 0, n) #define MD 1000000007 template T read(){T a;cin >> a;return a;} template void read(T& a){cin >> a;} template void rarr(T a, int n){for(int i = 0; i < n; i++) {cin >> a[i];}} template void write(T a){cout << a << endl;} template void writes(vector a, const char* c = " "){cout << a[0];for(int i = 1; i < (int)a.size(); i++)cout << c << a[i];cout << endl;;} void write(double a){cout << fixed << setprecision(12) << a << endl;} void write(long double a){cout << fixed << setprecision(12) << a << endl;} template void warr(T a, int n, const char* c = " "){cout << a[0];for(int i = 1; i < n; i++)cout << c << a[i];cout << endl;} void split(string s, string delim, veci& result){result.clear();string::size_type pos = 0;while(pos != string::npos){string::size_type p = s.find(delim, pos);if(p == string::npos){result.push_back(atoi(s.substr(pos).data()));break;}else {result.push_back(atoi(s.substr(pos, p - pos).data()));}pos = p + delim.size();}} void split(string s, string delim, vecs& result){result.clear();string::size_type pos = 0;while(pos != string::npos){string::size_type p = s.find(delim, pos);if(p == string::npos){result.push_back(s.substr(pos));break;}else {result.push_back(s.substr(pos, p - pos));}pos = p + delim.size();}} ll gcd(ll a, ll b){while(true){ll k = a % b;if(k == 0)return b;a = b;b = k;}} ll comb(ll n, ll m){ll p=1;m=min(m,n-m);for(ll i=1;i<=m;i++){p*=n-i+1;p/=i;}return p;} int main(void) { return 0; }