Template

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <algorithm>
#include <vector>
#include <map>
#include <set>
#include <bitset>
#include <queue>
#include <stack>
#include <valarray>
#include <sstream>
#include <cstring>
#include <numeric>
#include <ctime>
#include <cassert>

#define re return
#define fi first
#define se second
#define mp make_pair
#define pb emplace_back
#define all(x) x.begin(), x.end()
#define sz(x) ((int)(x).size())
#define rep(i, n) for (int i = 0; i < (n); i++)
#define rrep(i, n) for (int i = (n) - 1; i >= 0; i--)
#define y0 y32479
#define y1 y95874
#define next next239
#define prev prev239
#define fill(x, y) memset(x, y, sizeof(x))
#define sqr(x) ((x)*(x))
#define sqrt(x) sqrt(abs(x))
#define unq(x) (x.resize(unique(all(x)) - x.begin()))
#define ba back()
#define fastIO() {ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);}
#define read(x) int x; cin >> x;
#define read1(x) int x; cin >> x; x--;
#define readll(x) ll x; cin >> x;
#define reads(x) string x; cin >> x;

#ifdef LOCAL_BOBER
bool local = true;
#define deb(x) cout << #x << " = " << (x) << endl
#define debn(x, n) { cout << #x << "(" << n << ") = " << \
    "{"; int _f_ = 1; rep(_i_, n) {if (!_f_) cout << "|"; cout << x[_i_]; _f_= 0;} cout << "}" << endl;}
#define deba(x) { cout << #x << " (size: " << sz(x) << ") = " << \
    "{"; int _f_ = 1; for (auto o : x) {if (!_f_) cout << "|"; cout << o; _f_ = 0;} cout << "}" << endl;}
#else
bool local = false;
#define deb(x) ;
#define debn(x, n) ;
#define deba(x) ;
#define endl "\n"
#endif

using namespace std;

typedef vector<int> vi;
typedef vector<vi> vvi;
typedef pair<int, int> ii;
typedef vector<ii> vii;
typedef vector<string> vs;
typedef long long ll;
typedef pair<ll, ll> pll;
typedef vector<ll> vll;
typedef pair<double, double> pdd;
typedef long double LD;
typedef double D;

template<class T> string toString(T x) { ostringstream sout; sout << x; re sout.str();}
template<class T1, class T2> ostream& operator << (ostream &o, pair<T1, T2> x) {re o << x.fi << ' ' << x.se;}
template<class T1, class T2> istream& operator >> (istream &o, pair<T1, T2> &x) {re o >> x.fi >> x.se;}
template<class T1, class T2> pair<T1, T2> operator + (pair<T1, T2> a, pair<T1, T2> b) {a.fi += b.fi; a.se += b.se; re a;}
template<class T1, class T2> pair<T1, T2> operator - (pair<T1, T2> a, pair<T1, T2> b) {a.fi -= b.fi; a.se -= b.se; re a;}
template<class T1, class T2> void operator += (pair<T1, T2> &a, pair<T1, T2> b) {a.fi += b.fi; a.se += b.se;}
template<class T1, class T2> void operator -= (pair<T1, T2> &a, pair<T1, T2> b) {a.fi -= b.fi; a.se -= b.se;}
int nint() {int x; scanf("%d", &x); re x;}

double getTime() { re clock() / (double) CLOCKS_PER_SEC;};

const int mod = 1000000000 + 7;

void initIO() {
    if (local) {
        freopen("input.txt", "r", stdin);
        //freopen("output.txt", "w", stdout);
        srand((int)time(0));
    }
    else {
        //freopen("input.txt", "r", stdin);
        //freopen("output.txt", "w", stdout);
    }
    fastIO();
}


/* ============================= actual code starts here ============================= */

int m;
int n;
ll ans;

int main() {
    initIO();


}