#include<bits/stdc++.h>
#ifdef LOCAL
    #define _GLIBCXX_DEBUG
    #define dbg(x) cerr << #x << " = " << x << char(10);
#else
    #define dbg(x) ;
    #define cerr if(0) cerr
    // #pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math")
    // #pragma GCC target("sse,sse2,sse3,ssse3,sse4.1,sse4.2,avx,avx2,popcnt,tune=native")
#endif
#define forn(i, n) for (int i = 0; i < (int)(n); i++)
#define all(x) (x).begin(), (x).end()
#define pb push_back
#define mkt make_tuple
using namespace std;
using ld = long double;
using ll = long long;
using vi = vector<int>;
using vll = vector<ll>;
const ld eps = 1e-8l;
const int INF = 1e9 + 10;
const ll INFL = 9 * 1e18;
const ll MOD = 1e9 + 7;
const ld Pi = acosl(-1.0l);

int main()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.precision(9);
    cout << fixed;
    #ifdef LOCAL
        assert(freopen("in", "r", stdin));
        assert(freopen("out", "w", stdout));
        assert(freopen("err", "w", stderr));
    #endif


}