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.*;
import java.io.*;


public class Solution {

    class Pair {
        int color;
        int cnt;
        public Pair(int color, int cnt) {
            this.color = color;
            this.cnt = cnt;
        }
    }

    public int[] solution(int n, int color[]) {
        int[] result = new int[n];
        Pair[] pair = new Pair[n];
        for(int i = 0; i < n; ++i) {
            pair[i] = new Pair(i, 0);
        }
        for(int i = 0; i < n; ++i) {
            Pair max = new Pair(0, 0);
            for(int j = 0; j < n; ++j) {
                pair[j].cnt = 0;
            }
            for(int j = i; j < n; ++j) {
                pair[color[j]].cnt += 1;
                if(pair[color[j]].cnt > max.cnt) max = pair[color[j]];
                else if(pair[color[j]].cnt == max.cnt)
                    if(pair[color[j]].color < max.color) max = pair[color[j]];
                result[max.color]++;
            }
        }
        return result;
    }

    public static void main(String args[]) {
        Scanner cin = new Scanner(System.in);
        Solution s = new Solution();
        int n = cin.nextInt();
        int color[] = new int[n];
        for(int i = 0; i < n; ++i) {
            color[i] = cin.nextInt() - 1;
        }
        int result[] = s.solution(n, color);
        System.out.print(result[0]);
        for(int i = 1; i < n; ++i) System.out.print(" " + result[i]);
        System.out.println();
        cin.close();
    }
}

/**
 * Your TicTacToe object will be instantiated and called as such:
 * TicTacToe obj = new TicTacToe(n);
 * int param_1 = obj.move(row,col,player);
 */