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.TreeSet;

public class C {
	public static void main(String[] args) throws NumberFormatException, IOException {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		int len = Integer.parseInt(in.readLine());
		String[] line = in.readLine().split(" ");
		int[][] cumu = new int[len+1][len];
		int[] dom = new int[len];
		int[][] dominated = new int[len+1][len+1];
		for(int i = 1; i<=len; i++){
			for(int j =0;j<len;j++){
				cumu[i][j]+=cumu[i-1][j];
			}
			int here = Integer.parseInt(line[i-1])-1;
			cumu[i][here]++;
			for(int k = 0; k<i; k++){
				int best = cumu[i][here]-cumu[k][here];
				int bestI = here;
				int compare = dominated[i-1][k];
				int sum = cumu[i][compare]-cumu[k][compare];
				if(sum> best || (sum==best && compare<bestI)){
					best = sum;
					bestI = compare;
				}
				dom[bestI]++;
				dominated[i][k]=bestI;
			}
		}
		StringBuilder sb = new StringBuilder();
		sb.append(dom[0]);
		for(int i = 1; i<len; i++){
			sb.append(" "+dom[i]);
		}
		System.out.println(sb.toString());
	}
}
