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.BufferedWriter;
    	import java.io.IOException;
    	import java.io.InputStream;
    	import java.io.OutputStream;
    	import java.io.OutputStreamWriter;
    	import java.io.PrintWriter;
    	import java.io.Writer;
    	import java.util.Arrays;
    	import java.util.InputMismatchException;
    	import java.util.*;
    	import java.io.*;
    	import java.math.*;
    	public class Main7{
     
    	static class Pair
    		{ 
    			int x;
    			int y;
    			public Pair(int x,int y) 
    			{	 
    				this.x= x; 
    				this.y= y;
    			}	 
				
			@Override
					public int hashCode() 
					{ 
						final int temp = 14; 
						int ans = 1; 
						ans =x*31+y*13; 
						return ans; 
					} 
			  
					// Equal objects must produce the same 
					// hash code as long as they are equal 
				@Override
				public boolean equals(Object o) 
				{ 
					if (this == o) { 
						return true; 
					} 
					if (o == null) { 
						return false; 
					} 
					if (this.getClass() != o.getClass()) { 
						return false; 
					} 
					Pair other = (Pair)o; 
					if (this.x != other.x || this.y!=other.y) { 
						return false; 
					} 
					return true; 
				} 
					
    		} 
    		static class Pair1
    		{
    			String x;
    			int y;
    			int z;
    			
    		}
    		static class Compare
    		{ 
    			/*static 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) 
    					{ 
    						if(p1.start>p2.start)
    						{
    							return 1;
    						}
    						else if(p1.start==p2.start)
    						{
    							return 0;
    						}
    						else
    						{
    							return -1;
    						}
    					} 
    				}); 
    			}
    			*/
    		}
    		
    		
    		public static long pow(long a, long b)
    		{
    			long result=1;
    			while(b>0)
    			{
    				if (b % 2 != 0)
    				{
    					result=(result*a)%998244353;
    					b--;
    				} 
    				a=(a*a)%998244353;
    				b /= 2;
    			}   
    			return result;
    		}
    		public static long fact(long num)
    		{
    					long value=1;
    					int i=0;
    					for(i=2;i<num;i++)
    					{
    						value=((value%mod)*i%mod)%mod;
    					}
    					return value;
    				}
    				public static int gcd(int a, int b)
    				{
    					if (a == 0)
    						return b;
    					return gcd(b%a, a);
    				}
    				
    		/*		public static long lcm(long a,long b)
    				{
    					return a * (b / gcd(a, b));
    				}
    			*/	public static long sum(int h)
    				{
    					return (h*(h+1)/2);
    				}
    				public static void dfs(int parent,boolean[] visited,int[] dp)
    				{
    					ArrayList<Integer> arr=new ArrayList<Integer>();
    					arr=graph.get(parent);
    					visited[parent]=true;
    					for(int i=0;i<arr.size();i++)
    					{
    						int num=(int)arr.get(i);
    						if(visited[num]==false)
    						{
    							dfs(num,visited,dp);
							}
							dp[parent]=Math.max(dp[num]+1,dp[parent]);
    					}
    				}
    			//	static int flag1=0;
    				static int[] dis;
    				static int mod=1000000007;
    				static ArrayList<ArrayList<Integer>> graph;
    				
    				public static void bfs(int num,int size)
    				{
    					boolean[] visited=new boolean[size+1];
    					Queue<Integer> q=new LinkedList<>();
    					q.add(num);
    					ans[num]=1;
    					visited[num]=true;
    					while(!q.isEmpty())
    					{
    						int x=q.poll();
    						ArrayList<Integer> al=graph.get(x);
    						for(int i=0;i<al.size();i++)
    						{
    							int y=al.get(i);	
    							if(visited[y]==false)
    							{
    								q.add(y);
    								ans[y]=ans[x]+1;
    								visited[y]=true;
    							}
    						}
    					}
    				}
    				static int[] ans;
    				
    				
    				
    				
    				
    				
    				
    				
    				
    			//	static int[] a;			  
    				public static int[] sort(int[] a)
    				{
    					int n=a.length;
    					ArrayList<Integer> ar=new ArrayList<>();
    					for(int i=0;i<a.length;i++)
    					{
    						ar.add(a[i]);
    					}
    					Collections.sort(ar);
    					for(int i=0;i<n;i++)
    					{
    						a[i]=ar.get(i);
    					}
    					return a;
    				}
					static public void main(String args[])throws IOException
    				{
    		//		    BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
    			/*		boolean[] prime=new boolean[1101];
    					for(int i=2;i*i<=1100;i++)
    					{
    						if(prime[i]==false)
    						{
    							for(int j=2*i;j<=1100;j+=i)
    							{
    								prime[j]=true;
    							}
    						}
    					}*/
						int q=i();
						while(q-->0)
						{
							int n=i();
							int[] a=new int[4*n];
							int[] count=new int[100001];
							int max=0;
							int min=10000001;
							for(int i=0;i<4*n;i++)
							{
								a[i]=i();
								max=Math.max(a[i],max);
								min=Math.min(a[i],min);
								count[a[i]]++;
							}
							int ans=0;
							for(int i=0;i<=max;i++)
							{
								if(count[i]%2==1)
									ans++;
							}
							if(ans>0)
								pln("NO");
							else
							{
								a=sort(a);
								int i=0,j=4*n-1;
								int area1=a[0]*a[4*n-1];
								int area=0;
								while(i<j)
								{
									area=a[i]*a[j];
									if(area!=area1)
										ans++;
									i+=2;
									j-=2;
								}
								if(ans>0)
									pln("NO");
								else
									pln("YES");
							}
						}
					}
    				
    				
    				
    				/**/
    				static InputReader in=new InputReader(System.in);
    					static OutputWriter out=new OutputWriter(System.out);
    					public static long l()
    					{
    						String s=in.String();
    						return Long.parseLong(s);
    					}
    					public static void pln(String value)
    					{
    						System.out.println(value);
    					}
    					public static int i()
    					{
    						return in.Int();
    					}
    					public static String s()
    					{
    						return in.String();
    					}
    		}
    			 
    			 
    			 
    			 
    			 
    			 
    			 
    			 
    			 
    			 
    			 
    			 
    			 
    			 
    			 
    			 
    			 
    			 
    			 
    			 
    			 
    			 
    			class InputReader {
    				 
    				private InputStream stream;
    				private byte[] buf = new byte[1024];
    				private int curChar;
    				private int numChars;
    				private SpaceCharFilter filter;
    			 
    				public InputReader(InputStream stream) {
    					this.stream = stream;
    				}
    			 
    				public int read() {
    					if (numChars== -1)
    						throw new InputMismatchException();
    					if (curChar >= numChars) {
    						curChar = 0;
    						try {
    							numChars = stream.read(buf);
    						} catch (IOException e) {
    							throw new InputMismatchException();
    						}
    						if (numChars <= 0)
    							return -1;
    					}
    					return buf[curChar++];
    				}
    			 
    				public int Int() {
    					int c = read();
    					while (isSpaceChar(c))
    						c = read();
    					int sgn = 1;
    					if (c == '-') {
    						sgn = -1;
    						c = read();
    					}
    					int res = 0;
    					do {
    						if (c < '0' || c > '9')
    							throw new InputMismatchException();
    						res *= 10;
    						res += c - '0';
    						c = read();
    					} while (!isSpaceChar(c));
    					return res * sgn;
    				}
    			 
    				public String String() {
    					int c = read();
    					while (isSpaceChar(c))
    						c = read();
    					StringBuilder res = new StringBuilder();
    					do {
    						res.appendCodePoint(c);
    						c = read();
    					} while (!isSpaceChar(c));
    					return res.toString();
    				}
    			 
    				public boolean isSpaceChar(int c) {
    					if (filter != null)
    						return filter.isSpaceChar(c);
    					return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    				}
    			 
    				public String next() {
    					return String();
    				}
    			 
    				public interface SpaceCharFilter {
    					public boolean isSpaceChar(int ch);
    				}
    			}
    			 
    			class OutputWriter {
    				private final PrintWriter writer;
    			 
    				public OutputWriter(OutputStream outputStream) {
    					writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    				}
    			 
    				public OutputWriter(Writer writer) {
    					this.writer = new PrintWriter(writer);
    				}
    			 
    				public void print(Object...objects) {
    					for (int i = 0; i < objects.length; i++) {
    						if (i != 0)
    							writer.print(' ');
    						writer.print(objects[i]);
    					}
    				}
    			 
    				public void printLine(Object...objects) {
    					print(objects);
    					writer.println();
    				}
    			 
    				public void close() {
    					writer.close();
    				}
    			 
    				public void flush() {
    					writer.flush();
    				}
    			 
    				}
    			 
    				class IOUtils {
    			 
    				public static int[] readIntArray(InputReader in, int size) {
    					int[] array = new int[size];
    					for (int i = 0; i < size; i++)
    						array[i] = in.Int();
    					return array;
    				}
    			 
    				} 