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.util.*;
import java.text.*;
import java.lang.*;
import java.math.*;
 
public class Main{
    
    static int f(int i,int j) {
    	if(i==0) {   //up
    		if(j==0 || j==1) {
    			return 1;
    		}
    	}
    	else if(i==1) {
    		if(j==0 || j==1) {
    			return -1;
    		}
    	}
    	else if(i==3) {
    		if(j==2 || j==3) {
    			return 1;
    		}
    	}
    	else {
    		if(j==2 || j==3) {
    			return -1;
    		}
    	}
       return 0;
    }
       public void solve () {
        InputReader in = new InputReader(System.in);
        PrintWriter pw = new PrintWriter(System.out); 
        int t=in.nextInt();
        while(t-->0) {
	        int n=in.nextInt()*4;
	        Long a[]=new  Long [n];
	        for(int i=0;i<n;i++) {
	        	a[i]=in.nextLong();
	        }
	        Arrays.sort(a);
	        boolean chk=true;
	        if(!a[1].equals(a[0]) ||!a[n-1].equals(a[n-2])) {
	        	chk=false;
	        }
	        long maxi=a[0]*a[n-2];
	        for(int i=1;i<n/4;i++) {
	        	if(!a[2*i].equals(a[2*i+1]) || !a[n-(2*(1+i))].equals(a[n-(2*(i+1))+1])) {
		        	chk=false;
		        }
	        	long got=a[2*i]*a[n-(2*(1+i))];
	        	if(got!=maxi) chk=false;
	        }
	        if(chk) {
	        	pw.println("YES");
	        }
	        else {
	        	pw.println("NO");
	        }
        }
        pw.flush();
        pw.close();
    }
    public static void main(String[] args) throws Exception {
        
        
        new Thread(null,new Runnable() {
            public void run() {
                new Main().solve();
            }
        },"1",1<<26).start();
        
        
    }
    static class trie{
        trie x,y;
        Integer z;
        trie(int z){
            x=null;
            y=null;
            this.z=z;
        }
        public String toSring() {
        	return (z+" ");
        }
    }
    static void debug(Object... o) {
        System.out.println(Arrays.deepToString(o));
        }
        
        static class InputReader 
        {
        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private SpaceCharFilter filter;
 
        public InputReader(InputStream stream) 
        {
            this.stream = stream;
        }
        public int snext() 
        {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) 
            {
                curChar = 0;
                try 
                {
                    snumChars = stream.read(buf);
                } 
                catch (IOException e) 
                {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }
 
        public int nextInt() 
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = snext();
            }
            int res = 0;
            do 
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public long nextLong()
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-') 
            {
                sgn = -1;
                c = snext();
            }
            long res = 0;
            do 
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public int[] nextIntArray(int n) 
        {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) 
            {
                a[i] = nextInt();
            }
            return a;
        }
 
        public String readString()
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            StringBuilder res = new StringBuilder();
            do 
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isSpaceChar(c));
            return res.toString();
        }
 
        public String nextLine() 
        {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            StringBuilder res = new StringBuilder();
            do 
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isEndOfLine(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;
        }
 
        private boolean isEndOfLine(int c) 
        {
            return c == '\n' || c == '\r' || c == -1;
        }
 
        public interface SpaceCharFilter
        {
            public boolean isSpaceChar(int ch);
        }
    }
        public static long mod = 1000000007;
        public static int d;
        public static int p;
        public static int q;
        public void extended(int a,int b) {
            if(b==0) {
                d=a;
                p=1;
                q=0;
            }
            else
            {
                extended(b,a%b);
                int temp=p;
                p=q;
                q=temp-(a/b)*q;
            }
        }
        public static int binaryExponentiation(int x,int n)
        {
            int result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=result * x;
                x=x*x;
                n=n/2;
            }
            return result;
        }
        
        public static long binaryExponentiation(long x,long n)
        {
            long result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=result * x;
                x=x*x;
                n=n/2;
            }
            return result;
        }
        
        public static int modularExponentiation(int x,int n,int M)
        {
            int result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=(result * x)%M;
                x=(x%M*x)%M;
                n=n/2;
            }
            return result;
        }
        
        public static long modularExponentiation(long x,long n,long M)
        {
            long result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=(result%M * x%M)%M;
                x=(x%M * x%M)%M;
                n=n/2;
            }
            return result;
        }
        
        public static long modInverse(int A,int M)
        {
            return modularExponentiation(A,M-2,M);
        }
        
        public static long modInverse(long A,long M)
        {
            return modularExponentiation(A,M-2,M);
        }
        public static long[] shuffle(long[] a,Random gen)
        {
            int n = a.length;
            for(int i=0;i<n;i++)
            {
                int ind = gen.nextInt(n-i)+i;
                long temp = a[ind];
                a[ind] = a[i];
                a[i] = temp;
            }
            return a;
        }
        
        public static void swap(int a, int b){
            int temp = a;
            a = b;
            b = temp;
        }
        
        public static HashSet<Integer> primeFactorization(int n)
        {
            HashSet<Integer> a =new HashSet<Integer>();
            for(int i=2;i*i<=n;i++)
            {
                while(n%i==0)
                {
                    a.add(i);
                    n/=i;
                }
            }
            if(n!=1)
                a.add(n);
            return a;
        }
        
        public static void sieve(boolean[] isPrime,int n)
        {
            for(int i=1;i<n;i++)
                isPrime[i] = true;
            
            isPrime[0] = false;
            isPrime[1] = false;
            
            for(int i=2;i*i<n;i++)
            {
                if(isPrime[i] == true)
                {
                    for(int j=(2*i);j<n;j+=i)
                        isPrime[j] = false;
                }
            }
        }
        
        public static long GCD(long gcd,long x)
        {
            if(x==0)
                return gcd;
            else
                return GCD(x,gcd%x);
        }
        
        static class pair implements Comparable<pair>
        {
            Integer x;
            Integer y,z;
            Long val;
            pair(int x,int y,int z,long val)
            {
                this.x=x;
                this.y=y;
                this.z=z;
                this.val=val;
            }

            public int compareTo(pair o) {
                int result = x.compareTo(o.x);
                if(result==0)
                    result = y.compareTo(o.y);
                
                return result;
            }  
            
            public String toString()
            {
                return x+" "+y;
            }
            
            public boolean equals(Object o)
            {
                if (o instanceof pair)
                {
                    pair p = (pair)o;
                    return p.x == x && p.y == y ;
                }
                return false;
            }
            
            public int hashCode()
            {
                return new Double(x).hashCode()*31 + new Long(y).hashCode();
            }
        }
        
    
}

class dsu{
    int parent[];
    dsu(int n){
        parent=new int[n+1];
        for(int i=0;i<=n;i++)
        {
            parent[i]=i;
        }
    }
    int root(int n) {
        while(parent[n]!=n)
        { 
            parent[n]=parent[parent[n]];
            n=parent[n];
        }
        return n;
    }
    void union(int _a,int _b) {
        int p_a=root(_a);
        int p_b=root(_b);
        
            parent[p_a]=p_b;
        
            
    }
    boolean find(int a,int b) {
        if(root(a)==root(b))
            return true;
        else
            return  false;
    }
    
    
}
class Segment{ 
    int seg[]; 
    int a[];
    int lazy[];
    Segment (int n,int b[]){
        seg=new int[4*n];
        lazy=new int[4*n];
        a=new int[b.length];
        a=b.clone();
    }
    public void build(int node,int start,int end) {
        if(start==end) {
            seg[node]=a[start];
            return ;
        }
        int mid=(start+end)/2;
        build(2*node+1,start,mid);
        build(2*node+2,mid+1,end);
        seg[node]=seg[2*node+1]+seg[2*node+2];
    }
    public void update(int node,int start,int end,int id,int val) {
        if(start==end) {
            seg[node]=a[start]=val;
            return;
        }
        int mid=(start+end)/2;
        if(id>=start && id<=mid) {
            update(2*node+1,start,mid,id,val);
        }
        else
            update(2*node+2,mid+1,end,id,val);
        seg[node]=seg[2*node+1]+seg[2*node+2];
    }
    public int query(int node,int start,int end,int l,int r) {
        if(l>end || r<start)
            return 0;
        if(start>=l && end<=r)
            return seg[node];
        
        int  mid=(start+end)/2;
        return (query(2*node+1,start,mid,l,r)+query(2*node+2,mid+1,end,l,r));
    }
    public void updateRange(int node,int start,int end,int l,int r,int val) {
        if(lazy[node]!=0) {
            if(start!=end) {
                lazy[2*node+1]+=lazy[node];
                lazy[2*node+2]+=lazy[node];
            }
            lazy[node]=0;
        }
        if(l>end || r<start)
            return ;
        if(start>=l && end<=r) {
            seg[node]=(end-start+1)*val;
            if(start!=end) {
                lazy[2*node+1]+=val;
                lazy[2*node+2]+=val;
            }
            lazy[node]=0;
            return ;
        }
        int mid=(start+end)/2;
        updateRange(2*node+1,start,mid,l,r,val);
        updateRange(2*node+2,mid+1,end,l,r,val);
        seg[node]=seg[2*node+1]+seg[2*node+2];
    }
    public int queryRange(int node,int start,int end,int l,int r) {
        if(l>end || r<start)
            return 0;
        if(lazy[node]!=0) {
            seg[node]=(end-start+1)*lazy[node];
            if(start!=end) {
                lazy[2*node+1]+=lazy[node];
                lazy[2*node+2]+=lazy[node];
            }
            lazy[node]=0;
        }
        if(start>=l && end<=r)
            return seg[node];
        
        int  mid=(start+end)/2;
        return (query(2*node+1,start,mid,l,r)+query(2*node+2,mid+1,end,l,r));
    }
    
}
