#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <vector>
#include <cmath>
#include <set>
#include <fstream>
#include <cstring>
#include <string>
#include <algorithm>
#include <map>
#include <queue>
#include <iterator>
#include <iomanip>
#include <bitset>
#include <unordered_set>
#include <unordered_map>
using namespace std;

#define sqr(x) ((x)*(x))
#define cbr(x) ((x)*(x)*(x))
//#define max(a, b) (((a)<(b))? (b):(a))
//#define min(a, b) (((a)<(b))? (a):(b))
#define all(a) a.begin(), a.end()

#define _sp system("pause");
#define _ln cout << "------------------------------------------------\n";
#define FI(a, n) for(int i=a;i<n;i++)
#define FJ(a, n) for(int j=a;j<n;j++)
#define REP(a, b, c) for(int (c) = (a); (c) < (b); (c)++)
#define rep(a, b, c) for(int (c) = (a); (c) < (b); (c)++)
#define per(b, a, c) for(int (c) = (b); (c) >= (a); (c)--)

#define ll long long
#define ull unsigned long long
#define pii pair<int, int>
#define pll pair<ll, ll>
#define mp(a, b) make_pair((a), (b))
#define pb(a) push_back((a))
#define x first
#define y second

#define x1 sasimathx1
#define y1 sasimathy1

ll delbit(ll a, ll k) { return a & (~(1 << k)); }
int delbit(int a, int k) { return a & (~(1 << k)); }
bool getbit(ll a, ll k) { return 1 & (a >> k); }
bool getbit(int a, int k) { return 1 & (a >> k); }
ll setbit(ll a, ll k) { return a |= (1 << k); }
int setbit(int a, int k) { return a |= (1 << k); }

inline ll mulmod(ll x, ll n, ll _mod) { ll res = 0; while (n) { if (n & 1)res = (res + x) % _mod; x = (x + x) % _mod; n >>= 1; }return res; }
inline ll powmod(ll x, ll n, ll _mod) { ll res = 1; while (n) { if (n & 1)res = (res*x) % _mod; x = (x*x) % _mod; n >>= 1; }return res; }
inline ll gcd(ll a, ll b) { ll t; while (b) { a = a%b; t = a; a = b; b = t; }return a; }
inline int gcd(int a, int b) { int t; while (b) { a = a%b; t = a; a = b; b = t; }return a; }
inline ll lcm(ll a, ll b) { return a / gcd(a, b)*b; }
inline ll gcd(ll a, ll b, ll c) { return gcd(gcd(a, b), c); }
inline int gcd(int a, int b, int c) { return gcd(gcd(a, b), c); }
double dist(double ax, double ay, double bx, double by) { return sqrt(sqr(ax - bx) + sqr(ay - by)); }

//DBG
template<typename T, typename T2>void printarr(T  a[], T2 sz, T2 beg = 0) { for (T2 i = beg; i<sz; i++) cout << a[i] << " "; cout << endl; }
#define DBG(a)         cout<<#a<<"="<<(a)<<"\n"
#define DBG2(a,b)       cout<<#a<<"="<<(a)<<", "<<#b<<"="<<(b)<<"\n"
#define DBG3(a,b,c)     cout<<#a<<"="<<(a)<<", "<<#b<<"="<<(b)<<", "<<#c<<"="<<(c)<<"\n"

//Files
#define FILE_MODE(FILE) freopen(FILE".in", "r", stdin), freopen(FILE".out", "w", stdout)

//Constants
#define PI    3.1415926535897932
#define INF   1011111111
#define LLINF 1000111000111000111LL
#define eps   1e-14
#define mod   1000000007
//-------------------------------------------------
#define N 21

int main(){
     ios::sync_with_stdio(0);
     cin.tie(0);

     return 0;
}