//The is shensirui make
//保留所有版权 
//shensirui team make it
//传送门 https://hydro.ac/domain/join?target=AKNOI 
//I like OI 
//I like ICPC too
//I like lodo too
//I like IOI 


// C
#ifndef _GLIBCXX_NO_ASSERT
#include <cassert>
#endif
#include <cctype>
#include <cerrno>
#include <cfloat>
#include <ciso646>
#include <climits>
#include <clocale>
#include <cmath>
#include <csetjmp>
#include <csignal>
#include <cstdarg>
#include <cstddef>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>

#if __cplusplus >= 201103L
#include <ccomplex>
#include <cfenv>
#include <cinttypes>
#include <cstdalign>
#include <cstdbool>
#include <cstdint>
#include <ctgmath>
#include <cwchar>
#include <cwctype>
#endif

// C++

#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <exception>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iosfwd>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <locale>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <stdexcept>
#include <streambuf>
#include <string>
#include <typeinfo>
#include <utility>
#include <valarray>
#include <vector>
//other
#include<windows.h>
using namespace std;
void count_sort(int a[],int n){
	int cnt=0;
	queue<int> q;
	while(q.size()<n){
		for(int i=1;i<=n;i++){
			if(a[i]==cnt){
				q.push(a[i]);
			}
		}
		cnt++;
	}
	while(q.size()!=0){
		cout<<q.front()<<" ";
		q.pop();
	}
}
int r_to_10(string s,int n){
	int t=0,ans=0,w=1;
	int l=s.size();
	for(int i=l-1;i>=0;i--){
		if(s[i]>='0' && s[i]<='9'){
			t=s[i]-'0';			
		}else{
			t=s[i]-'A'+10;
		}
		ans+=t*w;
		w*=n;
	} 
	return ans;
} 
void say(string a) {
	int l = a.size();
	for (int i = 0; i < l; i++) {
		cout << a[i];
		Sleep(100);
	}
	printf("\n");
}
bool s(int n){
    if(n<=1){
        return 0;
    }
    for(int i=2;i*i<=n;i++){
        if(n%i==0){
            return 0;
        }
    }
    return 1;
}

string to_r(int x,int r){
	string t="";
	string p ="0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";
	if(x==0){
		return "0";
	}
	while(x!=0){
		t=p[x%r]+t;
		x/=r;
	} 
	return t;
}
void to_first(int x[],int b,int e){
	for(int i=b;i<=e;i++){
		if(i!=(e-1)){
			swap(x[i],x[i+1]); 
		} 
	}
} 
int to_find(int x[],int e,int l){
	for(int i=0;i<l;i++){
		if(x[i]==e){
			return i;
		}
	}
}
bool is_in(int x[],int e,int l){
	for(int i=0;i<l;i++){
		if(x[i]==e){
			return 1;
		}
	}
	return 0;
}
#if __cplusplus >= 201103L
#include <array>
#include <atomic>
#include <chrono>
#include <condition_variable>
#include <forward_list>
#include <future>
#include <initializer_list>
#include <mutex>
#include <random>
#include <ratio>
#include <regex>
#include <scoped_allocator>
#include <system_error>
#include <thread>
#include <tuple>
#include <typeindex>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>

#endif