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.
//package qwert2603.alg;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class q133532 {

    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int N = Integer.parseInt(br.readLine());
        String[] split = br.readLine().split(" ");
        int[] i = new int[N];
        for (int j = 0; j < N; j++) {
            i[j] = Integer.parseInt(split[j])-1;
        }
        int[] d = new int[N + 1];
        for (int j = 0; j < N; j++) {
            df(d, i, j);
        }
        StringBuilder stringBuilder = new StringBuilder();
        for (int j = 0; j < N; j++) {
            stringBuilder.append(d[j]).append(" ");
        }
        System.out.println(stringBuilder.toString());
    }

    private static void df(int[] d, int[] i, int b) {
        int[] m = new int[i.length];
        int mi = b;
        for (int j = b; j < i.length; j++) {
            ++m[i[j]];
            if (m[i[j]] > m[mi] || (m[i[j]] == m[mi] && i[j] < mi)) {
                mi = i[j];
            }
            ++d[mi];
        }
    }

}
