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.*;

/* Mighty Cohadar */
public class Charlie {

	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		int n = scanner.nextInt();
		assert 1 <= n && n <= 5000 : "out of range, n: " + n;
		int[] C = new int[n];
		for (int i = 0; i < n; i++) {
			C[i] = scanner.nextInt() - 1;
		}
		int[] D = new int[n];
		for (int l = 0; l < n; l++) {
			int[] N = new int[n];
			int d = C[l];
			N[d]++;
			D[d]++;
			for (int r = l+1; r < n; r++) {
				int c = C[r];
				N[c]++;
				if (N[d] < N[c]) {
					d = c;
				} else if (N[d] == N[c] && d > c) {
					d = c;
				}
				D[d]++;
			}
		}
		StringBuilder sb = new StringBuilder();
		for (int i = 0; i < n; i++) {
			sb.append(D[i]);
			sb.append(" ");
		}
		System.out.println(sb);
	}

	static String join(int[] A, String delimiter) {
		StringBuilder sb = new StringBuilder();
		for (int a : A) {
			sb.append(a);
			sb.append(delimiter);
		}
		if (sb.length() >= delimiter.length()) {
			sb.setLength(sb.length() - delimiter.length());
		}			
		return sb.toString();
	}

	static void debug(Object...os) {
		System.err.printf("%.65536s\n", Arrays.deepToString(os));
	}
	
}
