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 CodeforcesRound351VKCup2016Round3Div2EditionProblemB {


        static class Problem {


                Scanner reader;
                PrintWriter writer;

                Problem() {


                        reader = new Scanner(System.in);
                        writer = new PrintWriter(System.out);


                }

                void Run() {


                        Solution();


                        writer.close();


                }

                void Solution() {


                        int n = reader.nextInt(), res[] = new int[n + 1], t[] = new int[n], summary[][] = new int[n][n + 1];
                        for (int i = 0; i < n; i++)
                                t[i] = reader.nextInt();


                        for (int i = 0; i < n; i++) {
                                int Maximal = 0;
                                for (int j = i; j < n; j++) {
                                        summary[i][t[j]]++;
                                        if (summary[i][t[j]] > summary[i][Maximal] || (summary[i][t[j]] == summary[i][Maximal] && t[j] < Maximal))
                                                Maximal = t[j];
                                        res[Maximal]++;
                                }
                        }


                        for (int i = 1; i <= n; i++)
                                writer.print(res[i] + " ");


                }


        }

        public static void main(String args[]) {


                Problem B = new Problem();


                B.Run();


        }

        
}
