You are given 4n sticks, the length of the i-th stick is a_i.

You have to create n rectangles, each rectangle will consist of exactly 4 sticks from the given set. The rectangle consists of four sides, opposite sides should have equal length and all angles in it should be right. Note that each stick can be used in only one rectangle. Each stick should be used as a side, you cannot break the stick or use it not to the full length.

You want to all rectangles to have equal area. The area of the rectangle with sides a and b is a ⋅ b.

Your task is to say if it is possible to create exactly n rectangles of equal area or not.

You have to answer q independent queries.

Input

The first line of the input contains one integer q (1 ≤ q ≤ 500) — the number of queries. Then q queries follow.

The first line of the query contains one integer n (1 ≤ n ≤ 100) — the number of rectangles.

The second line of the query contains 4n integers a_1, a_2, ..., a_{4n} (1 ≤ a_i ≤ 10^4), where a_i is the length of the i-th stick.

Output

For each query print the answer to it. If it is impossible to create exactly n rectangles of equal area using given sticks, print "NO". Otherwise print "YES".

Example

Input


5
1
1 1 10 10
2
10 5 2 10 1 1 2 5
2
10 5 1 10 5 1 1 1
2
1 1 1 1 1 1 1 1
1
10000 10000 10000 10000


Output


YES
YES
NO
YES
YES


import java.io.*;
import java.math.*;
import java.util.*;


// @author : Dinosparton 

public class test2 {
	 
	   static class Pair{ 
		   int x;
		   int y;
		   
		   Pair(int x,int y){ 
			   this.x = x;
			   this.y = y;
			   
		   }
	   }
	  
	   
	   static class Compare { 
		   
		     void compare(Pair arr[], int n) 
		    { 
		        // Comparator to sort the pair according to second element 
		        Arrays.sort(arr, new Comparator<Pair>() { 
		            @Override public int compare(Pair p1, Pair p2) 
		            { 
		                return p1.x - p2.x; 
		            } 
		        }); 
		  
//		        for (int i = 0; i < n; i++) { 
//		            System.out.print(arr[i].x + " " + arr[i].y + " "); 
//		        } 
//		        System.out.println(); 
		    } 
		} 
	   
	   static class Graph {
		    private int V; // No. of vertices
		 
		    // Array  of lists for
		    // Adjacency List Representation
		    private LinkedList<Integer> adj[];
		 
		    // Constructor
		    @SuppressWarnings("unchecked") Graph(int v)
		    {
		        V = v;
		        adj = new LinkedList[v];
		        for (int i = 0; i < v; ++i)
		            adj[i] = new LinkedList();
		    }
		 
		    // Function to add an edge into the graph
		    void addEdge(int v, int w)
		    {
		        adj[v].add(w); // Add w to v's list.
		    }
		 
	   }
	   
	   static long dfs(int i,boolean vis[],Graph g,long a[]) {
		   
	        vis[i]=true;
	        long ans=a[i];
	        for(Integer e:g.adj[i]) {
	            if(!vis[e])
	            ans=Math.min(ans,dfs(e,vis,g,a));
	        }
	        return ans;
	    }
	   
	   public static void main(String[] args) throws Exception
	    {
		   try {
	        Scanner sc = new Scanner(System.in);
            
	        int tc = sc.nextInt();
	        
	        while(tc-->0){
	          int n = sc.nextInt();
	          
	          int N = 4*n;
	          
	          int[] arr = new int[N];
	          for(int i =0; i < N;++i)
	            arr[i] = sc.nextInt();
	     
	          Arrays.sort(arr);
	          
	          long area = arr[0] *arr[N-1];
	          
	          boolean check = true;
	          for(int i = 0; i < N/2; i+=2)
	          {
	            if((arr[i]!=arr[i+1]) || (arr[N-i-1]!=arr[N-i-2]) || arr[i]*arr[N-1-i] != area ){
	            check = false;
	            }
	          }
	          if(check == true)
	            System.out.println("YES");
	          else
	            System.out.println("NO");
	        }
		   }
		   catch(Exception e) { 
			   return;
		   }
	    }
}  




