#include<stdio.h>

#include<cmath>

#include<string>

#include<cstring>

#include<iostream>

#include<algorithm>

#include<stack>

#include<queue>

#include<vector>

#include<map>

#include<bitset>

#include<set>

#include<list>

#define GC getchar_unlocked

#define mod 1000000007

#define MAX(a,b) ({a>b?a:b;})

#define MIN(a,b) ({a>b?b:a;})

#define MP make_pair

#define PB push_back

#define max 100000

using namespace std;

typedef long long int ll;

typedef unsigned long long int ull;

vector <int> a[max+10];

queue<int> Q;

int color[max+10];

int val[max+10];

template<class T>inline T input(T x){char c=GC();x=0;T s=1;while(c<48||c>57){if(c=='-')s=-1;c=GC();}while(c>=48&&c<=57){x=(x<<3)+(x<<1)+c-48;c=GC();}return x*s;}

int main()

}