human
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.
The above is tricky. Write me a correct solution in PYTHON3.

=====
Write me a Python program to print n integers?
assistant
#Here is Python program to print n integers.

class CodeforcesTask643ASolution:
    def __init__(self):
        self.result = ''
        self.ball_count = 0
        self.colors = []

    def read_input(self):
        self.ball_count = int(input())
        self.colors = [int(x) for x in input().split(" ")]

    def process_task(self):
        color_results = [0 for x in range(self.ball_count)]
        for x in range(self.ball_count):
            cl_counts = [0 for x in range(self.ball_count)]
            best = 0
            best_id = -1
            for y in range(x, self.ball_count):
                cl_counts[self.colors[y] - 1] += 1
                if cl_counts[self.colors[y] - 1] > best:
                    best = cl_counts[self.colors[y] - 1]
                    best_id = self.colors[y] - 1
                elif cl_counts[self.colors[y] - 1] == best:
                    if best_id > self.colors[y] - 1:
                        best_id = self.colors[y] - 1
                color_results[best_id] += 1
        self.result = " ".join([str(x) for x in color_results])

    def get_result(self):
        return self.result

if __name__ == "__main__":
    Solution = CodeforcesTask643ASolution()
    Solution.read_input()
    Solution.process_task()
    print(Solution.get_result())