643_A. 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
# n=int(input())
# n,k=map(int,input().split())
'''l=0
r=10**13
while l+1<r:
    mid=(l+r)//2
    val=(max(0,b_b*mid-b)*rb+max(0,b_s*mid-s)*rs+max(0,b_c*mid-b)*rc)
    if val>money:
        r=mid
    if val<=money:
        l=mid'''
# arr=list(map(int,input().split()))
# n=int(input())
#if all([size%ele==0 for ele,size in s.items()]):
# n,k=map(int,input().split())
# arr=list(map(int,input().split()))
#from collections import Counter
#arr=sorted([(n-int(x),i) for i,x in enumerate(input().split())])
n=int(input())
arr=[int(q)-1 for q in input().split()]
ans=[0]*n
for i in range(n):
    cnt = [0] * n
    best=0
    for j in arr[i:]:
        cnt[j]+=1
        if cnt[j]>cnt[best] or j<best and  cnt[j]==cnt[best] :
            best = j
        ans[best]+=1

print(*ans)



```