//#pragma GCC target("avx2")
//#pragma GCC optimize("O3")
//#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
//#include <atcoder/all>

#define ll long long
#define ld long double

#define rep(i, n) for(int i = 0; i < n; ++i)
#define rep2(i, a, b) for(int i = a; i <= b; ++i)
#define rrep(i, a, b) for(int i = a; i >= b; --i)

#define pii pair<int, int>
#define pdd pair<double, double>
#define pll pair<ll, ll>
#define pld pair<ld,ld>

#define fi first
#define se second

#define pb push_back
#define eb emplace_back

#define vi vector<int>
#define vd vector<double>
#define vll vector<ll>
#define vld vector<ld>
#define vpii vector<pii>
#define vpdd vector<pdd>
#define vpll vector<pll>
#define vpld vector<pld>
#define vvi(a,b,c,d) vector<vector<int>> a(b,vector<int>(c,d));
#define vvll(a,b,c,d) vector<vector<ll>> a(b,vector<ll>(c,d));

#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define MAX(x) *max_element(all(x)) 
#define MIN(x) *min_element(all(x)) 
#define sz(a) ((ll)(a).size())

#define endl '\n'
using namespace std;
//using namespace atcoder;
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; }

const ll INF=1e18+1;
const int inf=1e9+1;
const double PI=acos(-1);
int dy[8] = {0,1,0,-1,-1,1,1,-1};
int dx[8] = {1,0,-1,0,1,1,-1,-1};

bool range(int y, int x, int h, int w){
  if(y < 0 || x < 0 || y >= h || x >= w) return false;
  else return true;
}

const int MOD=1000000007;
//using mint = modint1000000007;
//const int MOD=998244353;
//using mint = modint998244353;

const int M = 510000;


signed main(){
  cin.tie(0);
  ios::sync_with_stdio(false); 
  cout << fixed << setprecision(15);
  
  
  return 0;
}