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

public class colors {
	public static void main(String[] args) throws IOException {
		BufferedReader read = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(read.readLine());
		StringTokenizer token = new StringTokenizer(read.readLine());
		int[][] balls = new int[n][n];
		int[] b = new int[n];
		for (int i = 0; i < n; i++) {
			int t = Integer.parseInt(token.nextToken());
			balls[i][t - 1]++;
			b[i] = t - 1;
		}
		int[] colors = new int[n];
		for (int i = 0; i < n; i++) {
			int[] temp = new int[n];
			int max = -1;
			int maxColor = -1;
			for (int j = 0; j < n; j++) {
				temp[j] = balls[i][j];
				if (temp[j] > max) {
					max = temp[j];
					maxColor = j;
				}
			}
			colors[maxColor]++;
			for (int j = i + 1; j < n; j++) {
				/*System.out.print(i + " "+ j + "     ");
				for (int a = 0; a < n; a++) {
					System.out.print(temp[a] + " ");
				}
				System.out.print("      " + max + " " + maxColor);
				System.out.println();*/
				temp[b[j]]++;
				if (temp[b[j]] > max) {
					max = temp[b[j]];
					maxColor = b[j];
				} else if (temp[b[j]] == max && b[j] < maxColor) {
					max = temp[b[j]];
					maxColor = b[j];
				}
				colors[maxColor]++;
			}
		}
		for (int i = 0; i < n; i++) {
			System.out.print(colors[i] + " ");
		}
	}
}
