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.io.*;
import java.util.*;

public class Main {

	public static void main(String args[]) {

		Scanner in;
		try {
			in = new Scanner(new File("input.txt"));
		} catch (Exception e) {
			in = new Scanner(System.in);
		}

		int n = in.nextInt();

		int[] balls = new int[n+1];
		int[] colors = new int[n+1];

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

		for (int i = 1; i <= n; ++i) {

			int[] currentColors = new int[n+1];

			int dominating = 0;
			int dominatingIndex = 0;

			for (int j = 0; i + j <= n; ++j) {

				int currentColor = balls[i + j];
				++currentColors[currentColor];

				if (currentColors[currentColor] > dominating ||
					(currentColors[currentColor] == dominating && currentColor < dominatingIndex)) {
					dominating = currentColors[currentColor];
					dominatingIndex = currentColor;
				}

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