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A. Bear and Colors

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputBear 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 *t*_{i}.

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 *t*_{1}, *t*_{2}, ..., *t*_{n} (1 ≤ *t*_{i} ≤ *n*) where *t*_{i} 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.

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

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