673_C. Bear and Colors
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.
```python
def main():
    n = int(input())
    a = [int(i) for i in input().strip().split()]

    res = [0] * n

    for st in range(n):
        cnt = [0] * n
        x = 0
        y = 0
        for ed in range(st, n):
            cnt[a[ed] - 1] += 1
            if (cnt[a[ed] - 1] > x) or (cnt[a[ed] - 1] == x and a[ed] - 1 < y):
                x = cnt[a[ed] - 1]
                y = a[ed] - 1
            res[y] += 1

    print(" ".join(map(str, res)))

if __name__ == "__main__":
    main()
```