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.


import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class ProblemC {
    private IOManager io = new IOManager();

    private void solve() throws IOException {
        int n = io.rInts()[0];
        int[] colors = io.rInts();

        Map<Integer, Integer> globalCntByIdx = new HashMap<>();
        Map<Integer, Integer> localCntByIdx = new HashMap<>();
        for (int i = 0; i < n; i++) {
            int bestCount = Integer.MIN_VALUE;
            int bestIdx = Integer.MIN_VALUE;
            localCntByIdx.clear();
            for (int j = i; j < n; j++) {
                int cnt = localCntByIdx.getOrDefault(colors[j], 0) + 1;
                if (cnt == bestCount) {
                    bestIdx = Math.min(bestIdx, colors[j]);
                } else if (cnt > bestCount) {
                    bestCount = cnt;
                    bestIdx = colors[j];
                }
                localCntByIdx.put(colors[j], cnt);
                globalCntByIdx.put(bestIdx, globalCntByIdx.getOrDefault(bestIdx, 0) + 1);
            }
        }
        for (int i = 1; i <= n; i++) {
            int cnt = globalCntByIdx.getOrDefault(i, 0);
            System.out.print(cnt + " ");
        }

    }

    class IOManager {
        BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
        private static final String SEPARATOR = " ";

        private int[] rInts() throws IOException {
            String[] readLine = bf.readLine().split(SEPARATOR);
            int[] ret = new int[readLine.length];
            int idx = 0;
            for (String s : readLine) {
                ret[idx++] = Integer.parseInt(s);
            }
            return ret;
        }

        int[] rLong() throws IOException {
            String[] readLine = bf.readLine().split(SEPARATOR);
            int[] ret = new int[readLine.length];
            int idx = 0;
            for (String s : readLine) {
                ret[idx++] = Integer.parseInt(s);
            }
            return ret;
        }

        void print(int... objectArray) {
            for (Object o : objectArray) {
                System.out.print(o + SEPARATOR);
            }
            System.out.println();
        }
    }

    public static void main(String... args) throws IOException {
        new ProblemC().solve();
    }
}
