#include <bits/stdc++.h>
using namespace std;
#define nmod(a, n) (a % n + n) % n
#define fastio \
ios_base::sync_with_stdio(false); \
cin.tie(0);
#define inF freopen("input.txt", "r", stdin);
#define outF freopen("output.txt", "w", stdout);
#define sortv(v) sort(v.begin(), v.end());
#define sortvr(v) sort(v.begin(), v.end(), greater<int>());
#define rev(v) reverse(v.begin(), v.end());
#define pb push_back
#define all(a) a.begin(), a.end()
#define rep(i, n) for (int i = 0; i < int(n); ++i)
#define repp(i, m, n) for (int i = m; i < int(n); ++i)
#define vi vector<int>
#define umap unordered_map
#define vii vector<vector<int>>
#define ll long long
#define setp(n) cout << fixed << setprecision(n) ;
const double pi = acos(-1), eps = 1e-9;
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &s)
{
for (auto const &i : s)
os << i << " ";
return os;
}
template <typename T>
std::istream &operator>>(std::istream &is, std::vector<T> &s)
{
for (int i = 0; i < s.size(); i++)
is >> s[i];
return is;
}
void setIO(string s)
{
freopen((s + ".in").c_str(), "r", stdin);
freopen((s + ".out").c_str(), "w", stdout);
}
const int INF = 1e9;
int main()
{
fastio;
}