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.HashMap;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Controller controller = new Controller();
        controller.Input();
        controller.function();
    }
}

/**
 * Todo - Please put description here
 * Author - Chanh
 * Date - 5/11/2016
 * Time - 11:40 PM
 */
class OccurenceHashMap extends HashMap<Integer, Integer> {
    public void increase(Integer key) {
        if (super.containsKey(key)) {
            super.put(key, super.get(key) + 1);
            return;
        }
        super.put(key, 1);
    }
}

/**
 * Todo - Please put description here
 * Author - Chanh
 * Date - 5/11/2016
 * Time - 11:18 PM
 */
class Controller {
    int n;

    int[] colors;

    public void Input() {
        Scanner reader = new Scanner(System.in);

        n = reader.nextInt();
        colors = new int[n];

        for (int i = 0; i < n; i++) {
            colors[i] = reader.nextInt();
        }
    }


    public void function() {
        int[] count = new int[n];
        int[] color_number_occurence = new int[n];

        int dominantColor = 0;
        for (int j = 0; j < n; j++) {
            Arrays.fill(color_number_occurence, 0);
            for (int k = j; k < n; k++) {
                int color_number = colors[k];
                color_number_occurence[color_number - 1]++;

                if (color_number_occurence[dominantColor] < color_number_occurence[color_number - 1]
                        || ((color_number_occurence[dominantColor] == color_number_occurence[color_number - 1]) && dominantColor > color_number - 1)) {
                    dominantColor = color_number - 1;
                }
                count[dominantColor]++;
            }
        }

        Output(count);
    }

    public void Output(int count[]) {
        for (int i = 0; i < count.length; i++) {
            System.out.print(count[i] + " ");
        }
    }

    private int dominantColorIn(int i, int j) {
//        OccurenceHashMap color = new OccurenceHashMap();
//        for (; i <= j; i++) {
//            color.increase(colors[i]);
//        }
//        int dominantColor = 0;
//        int occurenceOfDominatantColor = 0;
//        for (OccurenceHashMap.Entry<Integer, Integer> entry : color.entrySet()) {
//            if (occurenceOfDominatantColor < entry.getValue()) {
//                dominantColor = entry.getKey();
//                occurenceOfDominatantColor = entry.getValue();
//            } else if (occurenceOfDominatantColor == entry.getValue()) {
//                if (dominantColor > entry.getKey())
//                    dominantColor = entry.getKey();
//            }
//        }
//        return dominantColor;
        return 0;

    }
}


