#include <bits/stdc++.h>
#define init_io ios_base::sync_with_stdio(false); cin.tie(NULL)
#define FOR(i, a, b, in) for (int i = (a); i < (b); i += in)
#define REP(i, a, b) for (int i = (a); i < (b); i++)
#define RFOR(i, a, b, in) for (int i = (a) - 1; i >= (b); i -= in)
#define RREP(i, a, b) for (int i = (a) - 1; i >= (b); 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
#define mem(a, b) memset(a, (b), sizeof(a))
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;


    
}