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 Div2_351_C {
	public static void main(String[] args) throws IOException {
		BufferedInputStream bis = new BufferedInputStream(System.in);
		BufferedReader br = new BufferedReader(new InputStreamReader(bis));
		PrintWriter out = new PrintWriter(System.out);
		String line;
		StringTokenizer st;
		while ((line = br.readLine()) != null && !line.equals("")) {
			int n = Integer.parseInt(line.trim());
			int [] balls = new int[n];
			st = new StringTokenizer(br.readLine());
			for (int i = 0; i < balls.length; i++) {
				balls[i] = Integer.parseInt(st.nextToken());
			}
			int [] result = new int[n+1];
			for(int left = 0;left < balls.length;left++) {
				int [] colorings = new int[n+1];
				int maxInd = balls[left];
				for(int right = left;right < balls.length;right++) {
					colorings[balls[right]]++;
					if(colorings[balls[right]] > colorings[maxInd] ||
							(colorings[balls[right]] == colorings[maxInd] && maxInd > balls[right])) {
						maxInd = balls[right];
					}
					result[maxInd]++;
				}
			}
			for(int i = 1;i < result.length;i++)
				out.print(result[i]+" ");
			out.println();
		}
		out.close();
	}
}