include <bits/stdc++.h>

// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")
// #pragma GCC target("avx2,bmi,bmi2,popcnt,lzcnt")
using namespace std;

define int long long

define ii pair<int,int>

define iii pair<int,ii>

define vi vector<int>

define vii vector<ii>

define mii map<int,int>

define fi first

define se second

define pb push_back

define mp make_pair

define lb lower_bound

define ub upper_bound

define ep emplace_back

define endl "\n"

define MASK(i) (1LL << (i))

define c_bit(i) __builtin_popcountll(i)

define BIT(x,i) ((x) & MASK(i))

define SET_ON(x,i) ((x) | MASK(i))

define SET_OFF(x,i) ((x) & ~MASK(i))

define oo 1e18

define __lcm(a,b) (1ll * ((a) / __gcd((a), (b))) * (b))

define sz(A) (int) A.size()

define FOR(i,l,r) for (int i=l;i<=r;i++)

define FOD(i,r,l) for (int i=r;i>=l;i--)

define FORR(i,l,r,k) for (int i=l;i<=r;i+=k)

define FODD(i,l,r,k) for (int i=l;i<=r;i-=k)

define fillchar(a,x) memset(a, x, sizeof (a))

define faster ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);

define NAME "a"

signed main()
{
faster;
//freopen(NAME".inp", "r", stdin);
//freopen(NAME".out", "w", stdout);
return 0;
}

// _ ___ _ _ ____ _ _ _ ___ _ _ __ __ _ _
// | | / _ \ | \ | | / || | | | / \ |_ || | | |\ \ / /| | | |
// | | | | | || | || | _ | || | / _ \ | | | | | | \ \ /\ / / | | | |
// | | | || || |\ || || || _ | / ___ \ | | | || | \ V V / | || |
// |_____| _/ || _| _||| ||// _|__| _/ _/_/ _/

//