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.*;
import java.util.*;

public class VKC {
    
    public static void main(String[] args)throws Exception{
        IO.init(System.in);
        
        int n = IO.nextInt();
        int d[] = new int[n]; 
       
        for(int i=0;i<n;++i){
            d[i] = IO.nextInt(); 
        }
         
        int[] ans = new int[n+1];
        HashMap<Integer, Integer> occurences = new HashMap<>();
        
        for(int i=0;i<n;++i){    
            
            occurences.clear();
            
            int best = 0;
            int bestCount=0; 
            
            for(int j=i;j<n;++j){   
                int color = d[j];  
                int v;
                if(!occurences.containsKey(color)){ 
                    occurences.put(color, 1);  
                    v = 1;
                }else{ 
                    v = occurences.get(color);
                    occurences.put(color, ++v);
                }  
                if(best==0){ 
                    best = color;
                    bestCount = v;
                }else{
                    if(v>bestCount){  
                        best = color;
                        bestCount = v;
                    }else if(v==bestCount && color<best){   
                        best = color;
                        bestCount = v;
                    }
                } 
                ans[best]++;
            } 
        }
        for(int i=1;i<=n;++i)IO.print(ans[i]+" ");
    }

    static class IO {
        static BufferedReader reader;
        static StringTokenizer tokenizer;
 
        static void init(InputStream input) {
            reader = new BufferedReader(new InputStreamReader(input) );
            tokenizer = new StringTokenizer("");
        }
 
        static String next() throws IOException {
            while ( ! tokenizer.hasMoreTokens() ) { 
                tokenizer = new StringTokenizer(reader.readLine() );
            }
            return tokenizer.nextToken();
        }

        static int nextInt() throws IOException {
            return Integer.parseInt( next() );
        }

        static double nextDouble() throws IOException {
            return Double.parseDouble( next() );
        }

        static void print(Object ... o){
            for(int i=0;i<o.length;++i){
                System.out.print(o[i]);
            }
        }

        static void println(Object ... o){
            for(int i=0;i<o.length;++i){
                System.out.print(o[i]);
            }
            System.out.println();
        }
    }
}

