|VK Cup 2016 - Round 3|
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.
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.
Print n integers. The i-th of them should be equal to the number of intervals where i is a dominant color.
1 2 1 2
7 3 0 0
1 1 1
6 0 0
In the first sample, color 2 is dominant in three intervals:
There are 7 more intervals and color 1 is dominant in all of them.