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.io.PrintWriter;
import java.util.StringTokenizer;

public class Balls {

    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter printWriter = new PrintWriter(System.out);
        int n = Integer.parseInt(br.readLine());
        int [] a = new int[n];
        StringTokenizer st = new StringTokenizer(br.readLine());
        for (int i = 0; i < n; i++) {
            a[i] = Integer.parseInt(st.nextToken()) - 1;
        }
        int[] ans = new int[n];
        for (int i = 0; i < n; i++) {
            int best = a[i];
            int [] count = new int[n];
            for (int j = i; j < n; j++) {
                count[a[j]]++;
                if (count[a[j]] > count[best] || (count[a[j]] == count[best] && a[j] < best)) {
                    best = a[j];
                }
                ans[best] ++;
            }
        }
        for (int i = 0; i < n; i++) {
            printWriter.print(ans[i] + " ");
        }
        printWriter.flush();
        printWriter.close();
    }
}