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.util.*;


    public class Main {
        static int n;
        static int m;
        static int[] colors;
        static Scanner input;
        static int top[];
        static int sum[];
        static int count[];

        public static void main(String[] args){
            input = new Scanner(System.in);
            n= input.nextInt();
            colors = new int[n+1];
            int[] ans = new int[n+1];
            for(int i=1;i<n+1;i++){
                colors[i]= input.nextInt();
            }
            top = new int[n+1];
            sum = new int[n+1];
            count = new int[n+1];
            int maxValue=1;
            int maxIndex=1;
            for (int i = 1; i < n+1; i++) {///right border
                maxIndex=0;
                maxValue=0;
               for(int j = i; j < n+1; j++) {// left border
                   count[colors[j]]++;

                    if(maxValue==count[colors[j]]){
                        if(colors[j]<maxIndex) {
                            maxValue = count[colors[j]];
                            maxIndex = colors[j];
                        }
                    }else if(maxValue<count[colors[j]]){
                            maxValue = count[colors[j]];
                            maxIndex = colors[j];
                    }

                    top[maxIndex]++;
                }

                for(int j=1;j<n+1;j++){
                    sum[j]+=top[j];
                    top[j]=0;
                    count[j]=0;
                }
            }
            for(int i=1;i<n+1;i++) {
                System.out.println(sum[i]);
            }
            System.exit(0);
        }
    }