#include <bits/stdc++.h>
using namespace std;

// Type aliases
using ll  = long long;
using ull = unsigned long long;
using ld  = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using vi  = vector<int>;
using vll = vector<ll>;
using vvi = vector<vi>;

// Constants
const int MOD = 1e9 + 7;
const int INF = 1e9;
const ll LINF = 1e18;
const ld EPS = 1e-9;
const ld PI = acos((ld)-1);

// Macros
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define sz(x) ((int)(x).size())
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define rep(i, a, b) for (int i = (a); i < (b); i++)
#define per(i, a, b) for (int i = (b) - 1; i >= (a); i--)

// Debug (compiles out when -DLOCAL is not set)
#ifdef LOCAL
#define dbg(...) cerr << "[" << #__VA_ARGS__ << "]: ", _dbg(__VA_ARGS__)
template<class T> void _dbg(T x) { cerr << x << endl; }
template<class T, class... A> void _dbg(T x, A... a) { cerr << x << ", "; _dbg(a...); }
template<class T> void _dbg(vector<T>& v) { for (auto& x : v) cerr << x << " "; cerr << endl; }
#else
#define dbg(...)
#endif

// I/O
template<class T> inline bool chmin(T& a, T b) { return b < a ? a = b, true : false; }
template<class T> inline bool chmax(T& a, T b) { return a < b ? a = b, true : false; }

void solve() {
    // solution here
}

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

    int t = 1;
    // cin >> t;
    while (t--) solve();

    return 0;
}