/*

written by Pankaj Kumar.

country:-INDIA

*/

#include <bits/stdc++.h>

using namespace std;

typedef long long ll ;

typedef set<pair<int,int>> spi;

typedef set<pair<ll,ll>> spl;

typedef vector<pair<int,int>> vpi;

typedef vector<int> vi;

typedef vector<ll> vl;

typedef vector<bool> vb;

typedef vector<char> vc;

typedef vector<pair<ll,ll>> vpl;

typedef vector<string> vs;

typedef map<int,int>mi;

typedef map<ll,ll> ml;

typedef set<string> ss;

typedef set<char>sc;

typedef set<int> si;

typedef set<ll> sl;

#define pan cin.tie(0);cout.tie(0);ios_base::sync_with_stdio(0);

// define values.

#define mod 1e9+7LL

#define phi 1.618

/* Bit-Stuff */

#define get_set_bits(a) (__builtin_popcount(a))

#define get_set_bitsll(a) ( __builtin_popcountll(a))

#define get_trail_zero(a) (__builtin_ctz(a))

#define get_lead_zero(a) (__builtin_clz(a))

#define get_parity(a) (__builtin_parity(a))

/* Abbrevations */

#define ff first

#define ss second

#define mp make_pair

#define line cout<<endl;

#define pb push_back

#define Endl "\n"

// loops

#define loop(i,start,end) for(ll i=ll(start);i<ll(end);i++)

#define loop0(num) for(ll i=0;i<ll(num);i++)

#define forin(arr,n) for(ll i=0;i<n;i++) cin>>arr[i];

// Some print

#define no cout<<"NO"<<endl;

#define yes cout<<"YES"<<endl;

#define cc ll test;cin>>test;while(test--)

// sort

#define all(V) (V).begin(),(V).end()

#define srt(V) sort(all(V))

#define srtGreat(V) sort(all(V),greater<ll>())

// function

ll power(ll x, ll y, ll p)

}

/* ascii value

A=65,Z=90,a=97,z=122 1=49

*/

/* -----------------------------------------------------------------------------------*/

// freopen("input.txt", "r", stdin);

// freopen("output.txt", "w", stdout);

int main()