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.util.*;
public class A
{
      public static void main(String ar[])
      {
            Scanner s=new Scanner(System.in);
            int n=s.nextInt();
            int a[]=new int[n];
            for(int i=0;i<n;i++)
             a[i]=s.nextInt();
             
            int c[]=new int[n+1];
            
            for(int i=0;i<n;i++)
            {
                  PriorityQueue<B> pq=new PriorityQueue<B>(n,new The_Comp());
                  HashMap<Integer,Integer> hs=new HashMap<Integer,Integer>();
                  for(int j=i;j<n;j++)
                  {
                        if(hs.containsKey(a[j]))
                         hs.put(a[j],1+hs.get(a[j]));
                        else
                         hs.put(a[j],1);
                        
                        B b1=new B(a[j],hs.get(a[j]));
                        pq.add(b1);
                        c[pq.peek().x]++;
                  }
            }
            for(int i=1;i<=n;i++)
             System.out.print(c[i]+" ");
         /*    System.out.println();
             PriorityQueue<B> p1=new PriorityQueue<B>(n,new The_Comp());
             p1.add(new B(1,1));
             p1.add(new B(1,2));
             p1.add(new B(2,1));
             p1.add(new B(2,2));
             while(!p1.isEmpty())
              System.out.println(p1.peek().x+" "+p1.poll().y);   */
             
      }
}

class B
{
      int x=0;int y=0;
      public B(int xx,int yy)
      { x=xx;  y=yy; }
}

class The_Comp implements Comparator<B>
{
      public int compare(B b1,B b2)
      {
            if(b1.y<b2.y)
             return 1;
            else if(b1.y==b2.y)
            {
            if(b1.x>b2.x)
             return 1;
            else if(b1.x==b2.x)
             return 0;
            else
             return -1;    
            }
            else
             return -1;
      }
}