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 C{
    static java.io.PrintStream out=System.out;
    void solve(int n, int[] t){
        int[] count=new int[n];
        for(int i=0; i<n; i++){
            int[] sub=new int[n];
            int max=1,c=t[i];
            for(int j=i; j<n; j++){
                sub[t[j]]++;
                if(sub[t[j]]>max || (sub[t[j]]==max && t[j]<c)){
                    max=sub[t[j]];
                    c=t[j];
                }
                count[c]++;
                //out.format("%d, %d, %s\n",i,j,Arrays.toString(count));
            }
        }
        for(int x:count)
            out.print(x+" ");
        out.println();
    }
    public static void main(String[] argin) {
        C inst = new C();
        Scanner in = new Scanner(System.in);
        while(in.hasNextInt()){
            int n = in.nextInt();
            int[] t = new int[n];
            for(int i=0; i<n; i++){
                t[i]=in.nextInt()-1;
            }
            inst.solve(n,t);
        }
    }
}

