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.Scanner;

public class TaskC {
    public static void main(String[] args){
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt();

        int[] balls = new int[n + 1];
        int[] colors = new int[n + 1];
        Arrays.fill(colors, 0);

        for(int i = 1; i <= n; i++){
            balls[i] = scan.nextInt();
        }

        for(int i = 1; i <= n; i++){
            int[] c = new int[n + 1];
            Arrays.fill(c, 0);

            int max = 0; int maxi = 0;

            for(int w = i; w <= n; w++) {
                c[balls[w]]++;

                if(c[balls[w]] == max) {
                    if(balls[w] < maxi){
                        max = c[balls[w]];
                        maxi = balls[w];
                    }
                }
                else if(c[balls[w]] > max){
                    max = c[balls[w]];
                    maxi = balls[w];
                }

                colors[maxi]++;
            }
        }


        for(int i = 1; i <= n; i++){
            System.out.print(colors[i]);
            if(i != n) System.out.print(" ");
        }

    }
}
