SaMer has written the greatest test case of all time for one of his problems. For a given array of integers, the problem asks to find the minimum number of groups the array can be divided into, such that the product of any pair of integers in the same group is a perfect square. 

Each integer must be in exactly one group. However, integers in a group do not necessarily have to be contiguous in the array.

SaMer wishes to create more cases from the test case he already has. His test case has an array A of n integers, and he needs to find the number of contiguous subarrays of A that have an answer to the problem equal to k for each integer k between 1 and n (inclusive).

Input

The first line of input contains a single integer n (1 ≤ n ≤ 5000), the size of the array.

The second line contains n integers a_1,a_2,...,a_n (-10^8 ≤ a_i ≤ 10^8), the values of the array.

Output

Output n space-separated integers, the k-th integer should be the number of contiguous subarrays of A that have an answer to the problem equal to k.

Examples

Input

2
5 5


Output

3 0


Input

5
5 -4 2 1 8


Output

5 5 3 2 0


Input

1
0


Output

1
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Random;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

@SuppressWarnings("unused")
public class Solution{
	
	static int n;
	static int[] a;
	
	public static void main(String[] args) throws IOException {
		FastScanner fs = new FastScanner();
    	PrintWriter out = new PrintWriter(System.out);
    	
    	int tt = 1;
    	outer:
    	while(tt-->0) {
    		
    		n = fs.nextInt();
    		a = fs.readArray(n);
    		
    		for(int i=0;i<n;i++) {
    			a[i] = signum(a[i])*normalize(Math.abs(a[i]));
    		}
    		
    		HashMap<Integer, Integer> map = new HashMap<>();
    		
    		int[] ans = new int[n+1];
    		
    		for(int i=0;i<n;i++) {
    			map.clear();
    			for(int j=i;j<n;j++) {
    				map.put(a[j], map.getOrDefault(a[j], 0)+1);
    				int f = map.size();
    				if(f>1 && map.containsKey(0)) f--;
    				ans[f]++;
    			}
    		}
    		
    		for(int i=1;i<=n;i++) out.print(ans[i]+" ");
    		out.println();
    		
    	}
    	
    	out.close();
    }
	
	
	static int normalize(int x) {
		int ans = 1;
		for(int i=2;i*i<=x;i++) {
			int cnt = 0;
			while(x%i==0) {
				x /= i; cnt++;
			}
			if(cnt%2==1) ans *= i;
		}
		if(x>1) ans *= x;
		return ans;
	}
	
	static int signum(int x) {
		if(x<0) return -1;
		else if(x>0) return 1;
		else return 0;
	}
	
	static final Random random=new Random();
    
    static <T> void shuffle(T[] arr) {
    	int n = arr.length;
    	for(int i=0;i<n;i++	) {
    		int k = random.nextInt(n);
    		T temp = arr[k]; arr[k] = arr[i]; arr[i] = temp;
    	}
    }
    
    	
    static void ruffleSort(int[] a) {
    	int n=a.length;//shuffle, then sort 
    	for (int i=0; i<n; i++) {
    		int oi=random.nextInt(n); int temp=a[oi];
    		a[oi]=a[i]; a[i]=temp;
    	}
    	Arrays.sort(a);
    }
    
    static void ruffleSort(long[] a) {
    	int n=a.length;//shuffle, then sort 
    	for (int i=0; i<n; i++) {
    		int oi=random.nextInt(n); long temp=a[oi];
    		a[oi]=a[i]; a[i]=temp;
    	}
    	Arrays.sort(a);
    }
   
  
    
    static void reverse(int[] arr, int l, int r) {
    	for(int i=l;i<l+(r-l)/2;i++){
    		int temp = arr[i]; arr[i] = arr[r-i+l-1]; arr[r-i+l-1] = temp;
    	}
    }
    
    static void reverse(long[] arr, int l, int r) {
    	for(int i=l;i<l+(r-l)/2;i++){
    		long temp = arr[i]; arr[i] = arr[r-i+l-1]; arr[r-i+l-1] = temp;
    	}
    }
    
    
    static <T> void reverse(T[] arr, int l, int r) {
    	for(int i=l;i<l+(r-l)/2;i++) {
    		T temp = arr[i]; arr[i] = arr[r-i+l-1]; arr[r-i+l-1] = temp;
    	}
    }
    	
    	
    static class FastScanner{
    	BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    	StringTokenizer st = new StringTokenizer("");
     
    	public String next(){
    		while(!st.hasMoreElements()){
    			try{
    				st = new StringTokenizer(br.readLine());
    			} catch(IOException e){
    				e.printStackTrace();
    			}
    		}
    		return st.nextToken();
    	}
    		
    	public String nextLine() throws IOException {
    		return br.readLine();
    	}
    		
    	public int nextInt(){
    		return Integer.parseInt(next());
    	}
     
    	public int[] readArray(int n){
    		int[] a = new int[n];
    		for(int i=0;i<n;i++)
    			a[i] = nextInt();
    		return a;
    	}
    		
    	public long nextLong() {
    		return Long.parseLong(next());
    	}
    		
    	public char nextChar() {
    		return next().toCharArray()[0];
    	}
    }


   	
}
