Bear Limak has n colored balls, arranged in one long row. Balls are numbered 1 through n, from left to right. There are n possible colors, also numbered 1 through n. The i-th ball has color ti.

For a fixed interval (set of consecutive elements) of balls we can define a dominant color. It's a color occurring the biggest number of times in the interval. In case of a tie between some colors, the one with the smallest number (index) is chosen as dominant.

There are <image> non-empty intervals in total. For each color, your task is to count the number of intervals in which this color is dominant.

Input

The first line of the input contains a single integer n (1 ≤ n ≤ 5000) — the number of balls.

The second line contains n integers t1, t2, ..., tn (1 ≤ ti ≤ n) where ti is the color of the i-th ball.

Output

Print n integers. The i-th of them should be equal to the number of intervals where i is a dominant color.

Examples

Input

4
1 2 1 2


Output

7 3 0 0 


Input

3
1 1 1


Output

6 0 0 

Note

In the first sample, color 2 is dominant in three intervals:

  * An interval [2, 2] contains one ball. This ball's color is 2 so it's clearly a dominant color. 
  * An interval [4, 4] contains one ball, with color 2 again. 
  * An interval [2, 4] contains two balls of color 2 and one ball of color 1. 



There are 7 more intervals and color 1 is dominant in all of them.
// Created by Whiplash99
import java.io.*;
import java.util.*;
public class D
{
    static class Freq implements Comparable<Freq>
    {
        int index,val;
        Freq(int index, int val)
        {
            this.index=index;
            this.val=val;
        }
        public int compareTo(Freq o)
        {
            if(this.val==o.val)
            {
                if(this.index<o.index)
                    return -1;
                return 1;
            }
            else if(this.val<o.val)
                return -1;
            return 1;
        }
    }
    public static void main(String[] args) throws IOException
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));

        int i,N;

        N=Integer.parseInt(br.readLine().trim());
        String s[]=br.readLine().trim().split(" ");
        int a[]=new int[N];
        for(i=0;i<N;i++)
          a[i]=Integer.parseInt(s[i])-1;

        int j;

        int b[]=new int[N];
        int max[]=new int[N];
        PriorityQueue<Freq> PQ=new PriorityQueue<>();
        HashMap<Integer,Integer> map=new HashMap<>();

        for(i=0;i<N;i++)
        {
            Arrays.fill(max,0);
            PQ.clear();
            map.clear();

            for(j=i;j<N;j++)
            {
                map.put(a[j],map.getOrDefault(a[j],0)-1);
                int f=map.get(a[j]);

                PQ.add(new Freq(a[j],f));
                max[a[j]]=f;

                while(true)
                {
                    int t=PQ.peek().index;
                    if(max[t]!=PQ.peek().val)
                        PQ.poll();
                    else
                    {
                        b[t]++;
                        break;
                    }
                }
            }
        }

        StringBuilder sb=new StringBuilder();

        for(i=0;i<N;i++)
            sb.append(b[i]).append(" ");

        sb.append("\n");
        System.out.println(sb);
    }
}