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 N_ = 5050;
int N, T[N_];
int C[N_];
int ans[N_];
int main() {
  scanf("%d", &N);
  for (int i = 1; i <= N; i++) {
    scanf("%d", &T[i]);
  }
  for (int i = 1; i <= N; i++) {
    fill(C, C + N + 1, 0);
    int best_c = 0, best_t = -1;
    for (int j = i; j <= N; j++) {
      int c = ++C[T[j]];
      if (c > best_c || (c == best_c && T[j] < best_t))
        best_c = c, best_t = T[j];
      ++ans[best_t];
    }
  }
  for (int i = 1; i <= N; i++) printf("%d ", ans[i]);
  return 0;
}
