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.*;
import java.math.*;
public class Solve4 {
  public static void main(String[] args) {
	MyScanner scanner = new MyScanner();
	PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
	int n = scanner.nextInt();
	int[] tab = new int[n];
	for(int i = 0; i < n; i++) {
	  int a = scanner.nextInt()-1;
	  tab[i]= a;
	}
    int[] counts = new int[n];
	int [] t = new int[n];
	for(int i = 0; i < n; i++) {
	  Arrays.fill(t, 0);
	  int max_ind = 0;
	  for(int j = i; j < n; j++) {
	    int k = tab[j];
		t[k]++;
		int l = t[k];
		int before = t[max_ind];
		//System.out.println(l + " " + before);
		if(l > before || (l == before && k < max_ind)) {
		  max_ind = k;
		}
		//System.out.println(max_ind);
		counts[max_ind]++;
	  }
	}
	for(int i = 0; i < n; i++) {
		out.print(counts[i] + " ");
	}
	out.close();
  }


  public static class MyScanner {
      BufferedReader br;
      StringTokenizer st;
 
      public MyScanner() {
         br = new BufferedReader(new InputStreamReader(System.in));
      }
 
      String next() {
          while (st == null || !st.hasMoreElements()) {
              try {
                  st = new StringTokenizer(br.readLine());
              } catch (IOException e) {
                  e.printStackTrace();
              }
          }
          return st.nextToken();
      }
 
      int nextInt() {
          return Integer.parseInt(next());
      }
 
      long nextLong() {
          return Long.parseLong(next());
      }
 
      double nextDouble() {
          return Double.parseDouble(next());
      }
 
      String nextLine(){
          String str = "";
	  try {
	     str = br.readLine();
	  } catch (IOException e) {
	     e.printStackTrace();
	  }
	  return str;
      }

   }
}
