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;
int solve() {
  int n;
  cin >> n;
  int t[n];
  for (int i = 0; i < n; i++) {
    cin >> t[i];
    t[i]--;
  }
  int ans[n];
  for (int i = 0; i < n; i++) ans[i] = 0;
  for (int i = 0; i < n; i++) {
    int c[n];
    for (int j = 0; j < n; j++) {
      c[j] = 0;
    }
    int cm = 0;
    int cc = -1;
    for (int j = i; j < n; j++) {
      c[t[j]]++;
      if (c[t[j]] > cm) {
        cc = t[j];
        cm = c[t[j]];
      } else if (c[t[j]] == cm) {
        if (t[j] < cc) {
          cc = t[j];
          cm = c[t[j]];
        }
      }
      ans[cc]++;
    }
  }
  for (int i = 0; i < n; i++) cout << ans[i] << ' ';
  return 0;
}
int main() { solve(); }
