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.io.*;
import java.util.*;

public class Solution {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
		int[] arr = new int[n];
		for(int io=0;io<n;io++) arr[io] = sc.nextInt();
		int[] output = new int[n];
		int[] c = new int[n];
		for(int i=0;i<n;i++) output[i] = 0;
		for(int i=0;i<n;i++){
			int dom = arr[i]-1;
			for(int io=0;io<n;io++) c[io] = 0;
			for(int j=i;j<n;j++){
				int k = arr[j]-1;
				c[k] = c[k] + 1;
				if(k==dom){
				}else{
					if(c[k]>c[dom]){
						dom = k;
					}else{
						if(c[k]==c[dom]){
							if(k < dom) dom = k;
						}
					}
				}
				output[dom] = output[dom] + 1;
			}
		}
		for(int i=0;i<n;i++) System.out.print(output[i]+" ");
    }
}