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.BufferedWriter;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;

public class NewClass {
    public static void main(String[] args) throws Exception {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));
        int n = ip(in.readLine());
        int[] t = ia(in.readLine(), n);
        int[] count;
        int[] num = new int[n];
        for (int i=0; i<n; i++) {
            count = new int[n];
            int max=count[t[i]-1];
            for (int j=i; j<n; j++) {
                count[t[j]-1]++;
                if (count[t[j]-1]>count[max]) {
                    max = t[j]-1;
                }
                else if (count[t[j]-1]==count[max]) {
                    max = Math.min(t[j]-1, max);
                }
                num[max]++;
            }
        }
        for (int i=0; i<n; i++) {
            out.write(num[i]+" ");
        }
        out.write("\n");
        out.flush();
    }
    
    private static int ip (String s) {
        int n = Integer.parseInt(s);
        return n;
    }
    
    private static long lp(String s) {
        long n = Long.parseLong(s);
        return n;
    }
    
    private static double dp (String s) {
        double n = Double.parseDouble(s);
        return n;
    }
    
    private static int[] ia (String s, int n) {
        String[] s1 = s.split(" ");
        int[] A = new int[n];
        for (int i=0; i<n; i++) {
            A[i] = Integer.parseInt(s1[i]);
        }
        return A;
    }
    
    private static long[] la (String s, int n) {
        String[] s1 = s.split(" ");
        long[] A = new long[n];
        for (int i=0; i<n; i++) {
            A[i] = Long.parseLong(s1[i]);
        }
        return A;
    }
    
    private static double[] da(String s, int n) {
        String[] s1 = s.split(" ");
        double[] A = new double[n];
        for (int i=0; i<n; i++) {
            A[i] = Double.parseDouble(s1[i]);
        }
        return A;
    }

}