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>
using namespace std;
const int maxn = 5010;
int balls[maxn];
int n;
int main() {
  cin >> n;
  for (int i = 0; i < (int)(n); i++) {
    scanf("%d", &balls[i]);
    balls[i]--;
  }
  int ans[n];
  fill(ans, ans + n, 0);
  for (int start = 0; start < (int)(n); start++) {
    int tracking[n];
    fill(tracking, tracking + n, 0);
    int maxcolor = balls[start];
    int maxcnt = 1;
    tracking[maxcolor]++;
    ans[maxcolor]++;
    for (int i = start + 1; i < n; i++) {
      tracking[balls[i]]++;
      if (tracking[balls[i]] > maxcnt) {
        maxcolor = balls[i];
        maxcnt = tracking[balls[i]];
      } else if (tracking[balls[i]] == maxcnt) {
        if (balls[i] < maxcolor) maxcolor = balls[i];
      } else if (maxcolor == balls[i])
        maxcnt++;
      ans[maxcolor]++;
    }
  }
  for (int i = 0; i < (int)(n); i++) {
    cout << ans[i] << ' ';
  }
  cout << '\n';
  return 0;
}
