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.Scanner;

public class C {
    public static void main(String[] args) {
        Scanner input = new Scanner(new BufferedInputStream(System.in));
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        PrintStream output = new PrintStream(new BufferedOutputStream(System.out));

        int n = input.nextInt();
        int[] balls = new int[n];
        for(int i = 0; i < n; i++){
            balls[i] = input.nextInt();
        }
        int[] ans = new int[n + 1];
        for(int i = 0; i <= n; i++){
            ans[i] = 0;
        }
        int[] count = new int[n + 1];
        for(int i = 0; i < n; i++){
            for(int j = 0; j <= n; j++){
                count[j] = 0;
            }
            int max = 0;
            int ind = 0;
            for(int j = i; j < n; j++){
                count[balls[j]]++;
                if(count[balls[j]] > max || (count[balls[j]] == max && balls[j] < ind)){
                    max = count[balls[j]];
                    ind = balls[j];
                }
                ans[ind]++;
            }
        }

        for(int i = 1; i <= n; i++){
            output.print(ans[i] + " ");
        }
        output.println();

        output.close();
    }
}
