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.
from collections import defaultdict

def compare(a, b):
	if a[0] > b[0]:
		return True
	elif a[0] == b[0]:
		return a[1] < b[1]
	else:
		return False

def solve(colors):

	color_dict = defaultdict(int)
	for i in range(len(colors)):
		color_count = defaultdict(int)	
		majority = (1, colors[i])
		color_count[colors[i]] += 1
		# interval [i, i] = color[i]
		color_dict[colors[i]] += 1

		# interval [i, j], j > i
		for j in range(i+1, len(colors)):

			color_count[colors[j]] += 1
			if compare((color_count[colors[j]], colors[j]), majority):
				majority = (color_count[colors[j]], colors[j])
				color_dict[colors[j]] += 1
			else:
				color_dict[majority[1]] += 1

	ans = ''
	for color in range(len(colors)):
		ans += str(color_dict[color+1]) + ' '
	return ans.strip()

n = input()
colors = map(int, raw_input().split())
print solve(colors)