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#include <algorithm>
#include <iostream>
#include <fstream>
#include <string>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <cmath>
#include <cstring>
#define pname (string)""
#define init_io ifstream cin(pname+".in"); ofstream cout(pname+".out"); ios_base::sync_with_stdio(false); cin.tie(NULL)
#define FOR(i, a, b) for (int i = (a); i < (b); i++)
#define F0R(i, a) for (int i = 0; i < (a); i++)
#define FORd(i, a, b) for (int i = (b) - 1; i >= (a); i--)
#define F0Rd(i, a) for (int i = (a) - 1; i >= 0; i--)
#define trav(a, x) for (auto& a : x)
#define mp make_pair
#define pb push_back
#define f first
#define s second
#define lb lower_bound
#define ub upper_bound
#define sz(x) (int)x.size()
#define all(x) begin(x), end(x)
#define rsz resize
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> ii, typedef pair<ll, ll> pl, typedef pair<ld, ld> pd;
typedef vector<int> vi, typedef vector<ll> vl, typedef vector<ld> vd;
typedef vector<ii> vii, typedef vector<pl> vpl, typedef vector<pd> vpd;
constexpr auto INF = (int)1e9;
constexpr auto LINF = (ll)1e18;

int main() {
    init_io;


    
}