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;
struct store {
  store() { data = 0; }
  int data;
};
class Bear_and_Colors {
 public:
  void algorithm() {
    input();
    count();
    output();
  }

 private:
  int num_ball, *ball;
  store *result;
  int temp;
  void input() {
    cin >> num_ball;
    num_ball;
    ball = new int[num_ball + 1];
    for (int i = 1; i <= num_ball; i++) cin >> ball[i];
    result = new store[num_ball + 1];
  }
  void count() {
    for (int i = 1; i <= num_ball; i++) {
      store *interval = new store[num_ball + 1];
      temp = ball[i];
      for (int j = i; j <= num_ball; j++) {
        interval[ball[j]].data++;
        if (interval[ball[j]].data > interval[temp].data)
          temp = ball[j];
        else if (interval[ball[j]].data == interval[temp].data &&
                 ball[j] < temp)
          temp = ball[j];
        result[temp].data++;
      }
    }
  }
  void output() {
    for (int i = 1; i <= num_ball; i++) cout << result[i].data << " ";
    cout << endl;
  }
};
int main() {
  Bear_and_Colors test;
  test.algorithm();
  return 0;
}
