/* -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.

* Created By : Aditya Agarwal

* IT, MNNIT-ALLAHABAD

* aditya.mnnit15@gmail.com

_._._._._._._._._._._._._._._._._._._._._.*/

#include<bits/stdc++.h>

using namespace std;

#define MP make_pair

#define pb push_back

#define rep(i,n) for(int i=0;i<n;i++)

#define REP(i,a,b) for(int i=a;i<=b;i++)

#define PER(i,a,b) for(int i=b;i>=a;i--)

#define X first

#define Y second

#define all(c) c.begin(),c.end() //eg sort(all(v));

typedef long long ll;

typedef vector<int> vi;

typedef vector< vi > vvi;

typedef pair< int,int > ii;

#define sz(a) int((a).size())

#define clr(a) memset(a,0,sizeof(a))

#define ini(a) memset(a,-1,sizeof(a))

//i/o

#define inp(n) scanf("%d",&n)

#define inpll(n) scanf("%lld",&n)

#define inp2(n,m) inp(n), inp(m)

#define ins(s) scanf("%s",s);

#define out(n) printf("%d\n",n)

#define outll(n) printf("%lld\n",n)

#define out2(n,m) printf("%d %d\n",n,m)

#define inc(n) scanf("%c",&n)

//cost

#define MOD 1000000007

#define MOD_INV 1000000006

#define MAX 100009

#define INF 999999999

#define mp make_pair

#define pairs pair< pair<int,int>,int>

typedef long long ll;

int val[100001],par[100001];

int s[100001];

queue<pairs> q;

int level[100001];

pairs bfs(int n){

}

int main(){

}