import java.util.*;
import java.io.*;
import java.math.*;
public class loser
{
    static class InputReader {
        public BufferedReader br;
        public StringTokenizer token;
        public InputReader(InputStream stream)
        {
            br=new BufferedReader(new InputStreamReader(stream),32768);
            token=null;
        }

        public String next()
        {
            while(token==null || !token.hasMoreTokens())
            {
                try
                {
                    token=new StringTokenizer(br.readLine());
                }
                catch(IOException e)
                {
                    throw new RuntimeException(e);
                }
            }
            return token.nextToken();
        }

        public int nextInt()
        {
            return Integer.parseInt(next());
        }

        public long nextLong()
        {
            return Long.parseLong(next());
        }
    }
    static class card{
        int l;
        int r;
        public card(int ch,int i)
        {
            this.l=ch;
            this.r=i;
        }
    }
    static class sort implements Comparator<card>
    {
        public int compare(card o1,card o2)
        {
            if(o1.l!=o2.l)
                return (int)(o1.l-o2.l);
            else
                return (int)(o1.r-o2.r);
        }
    }
    static void shuffle(long a[])
    {
        List<Long> l=new ArrayList<>();
        for(int i=0;i<a.length;i++)
            l.add(a[i]);
        Collections.shuffle(l);
        for(int i=0;i<a.length;i++)
            a[i]=l.get(i);
    }

    /*static long gcd(long a,long b)
    {
    if(b==0)
    return a;
    else
    return gcd(b,a%b);
    }
    static int ans1=Integer.MAX_VALUE,ans2=Integer.MAX_VALUE,ans3=Integer.MAX_VALUE,ans4=Integer.MAX_VALUE;
    static boolean v[]=new boolean[101];
    static void dfs(Integer so,Set<Integer> s[]){
    if(!v[so.intValue()])
    {
    v[so]=true;
    for(Integer h:s[so.intValue()])
    {
    if(!v[h.intValue()])
   ... What is the time complexity of the previous code?