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.Scanner;

public class cf673c {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] colors = new int[n];
        int[] result = new int[n];
        for (int i=0; i < n; i++){
            colors[i] = sc.nextInt() - 1;
        }

        for (int i=0; i < n; i++) {
            int[] i_counts = new int[n];
            int best_c = 0;
            for (int j=i; j < n; j++) {
                i_counts[colors[j]] += 1;
                if (i_counts[colors[j]] > i_counts[best_c] | (i_counts[colors[j]] == i_counts[best_c] & best_c > colors[j])) {
                    best_c = colors[j];
                }
                result[best_c] += 1;
            }
        }

        for(int i=0; i<n; i++)
            System.out.print(result[i]+" ");
    }

}
