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.


import java.util.Arrays;
import java.util.HashMap;
import java.util.Scanner;

/**
 * @author Tony Stark
 */
public class A {
    public static void main(String[] args) {
        Scanner cin = new Scanner(System.in);
        int n = cin.nextInt();
        int a[] = new int[n + 1];
        int sonlar[] = new int[n + 1];
        int position[] = new int[n + 1];
        for(int i = 1 ; i <= n ;i ++){
            a[i] = cin.nextInt();
            if(position[a[i]] == 0)
                position[a[i]] = i;
        }

        for(int i = 1 ; i <= n ;i ++){
            int cnt = 0,maxe = 0;
            HashMap<Integer,Integer> hashMap = new HashMap<>();
            for(int j = i  ; j <= n;j ++){
                   hashMap.put(a[j],hashMap.get(a[j]) == null ? 1 : hashMap.get(a[j]) + 1);
                   if(hashMap.get(a[j]) > cnt){
                       cnt = hashMap.get(a[j]);
                       maxe = a[j];
                   }else{
                       if(hashMap.get(a[j]) == cnt && a[j] < maxe ){
                           maxe = a[j];
                       }
                   }
                   sonlar[maxe] ++;
            }
        }
        for(int i = 1 ; i <= n ;i++){
            System.out.print(sonlar[i]+" ");
        }


    }
}
