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.
#include <bits/stdc++.h>
const int N = 5010;
int color[N];
int color_count[N];
int color_interval[N];
int main() {
  int n;
  while (~scanf("%d", &n)) {
    for (int i = 0; i < n; ++i) {
      scanf("%d", color + i);
    }
    memset(color_interval, 0, sizeof(color_interval));
    for (int i = 0; i < n; ++i) {
      memset(color_count, 0, sizeof(color_count));
      int max_cnt(-9999999), max_id(-99999999);
      for (int j = i; j < n; ++j) {
        ++color_count[color[j]];
        if (max_cnt < color_count[color[j]]) {
          max_cnt = color_count[color[j]];
          max_id = color[j];
        } else if (max_cnt == color_count[color[j]] && max_id > color[j]) {
          max_id = color[j];
        }
        ++color_interval[max_id];
      }
    }
    for (int i = 1; i <= n; ++i) {
      if (i == 1)
        printf("%d", color_interval[i]);
      else
        printf(" %d", color_interval[i]);
    }
    printf("\n");
  }
  return 0;
}
