#D5674. Bear and Colors
Bear and Colors
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 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.
inputFormat
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.
outputFormat
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.
样例
3
1 1 1
6 0 0