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.PrintWriter;
import java.util.Arrays;
import java.util.Scanner;

/**
 * Created by fatminmin on 5/8/16.
 */
public class PC {
    Scanner sc = new Scanner(System.in);
    PrintWriter pw = new PrintWriter(System.out);
    public void run() {
        int n = sc.nextInt();
        int[] arr = new int[n];
        for(int i = 0; i < n; i++) {
            arr[i] = sc.nextInt() - 1;
        }
        int[] ans = new int[n];
        int[] mem = new int[n];
        for(int i = 0; i < n; i++) {
            Arrays.fill(mem, 0);
            int maxIdx = -1;
            int maxHere = 0;
            for(int j = i; j < n; j++) {
                mem[arr[j]]++;
                if(mem[arr[j]] > maxHere || (mem[arr[j]] == maxHere && arr[j] < maxIdx)) {
                    maxHere = mem[arr[j]];
                    maxIdx = arr[j];
                }
                ans[maxIdx]++;
            }
        }
        for(int i = 0; i < n; i++) {
            if(i > 0) pw.print(" ");
            pw.print(ans[i]);
        }
        pw.println();
        pw.flush();
    }

    public static void main(String[] args) {
        new PC().run();
    }
}
