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.
import math
import sys
from collections import Counter

def solve():
    n = int(input())
    T = [int(x) - 1 for x in input().split()]
    M = [[0]*n for i in range(n)]
    curmin, ans = [0]*n, [0]*n
    for i in range(n):
        ans[T[i]] += 1
        curmin[i] = T[i]
        M[i][T[i]] = 1

    for i in range(n):
        for j in range(i + 1, n):
            M[i][T[j]] += 1
            if (M[i][T[j]] > M[i][curmin[i]] or
                M[i][T[j]] == M[i][curmin[i]] and T[j] < curmin[i]):
                curmin[i] = T[j]
            ans[curmin[i]] += 1

    return ans
    

print(' '.join(map(str, solve())))

