Long time ago there was a symmetric array a_1,a_2,…,a_{2n} consisting of 2n distinct integers. Array a_1,a_2,…,a_{2n} is called symmetric if for each integer 1 ≤ i ≤ 2n, there exists an integer 1 ≤ j ≤ 2n such that a_i = -a_j.

For each integer 1 ≤ i ≤ 2n, Nezzar wrote down an integer d_i equal to the sum of absolute differences from a_i to all integers in a, i. e. d_i = ∑_{j = 1}^{2n} {|a_i - a_j|}.

Now a million years has passed and Nezzar can barely remember the array d and totally forget a. Nezzar wonders if there exists any symmetric array a consisting of 2n distinct integers that generates the array d.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases. 

The first line of each test case contains a single integer n (1 ≤ n ≤ 10^5).

The second line of each test case contains 2n integers d_1, d_2, …, d_{2n} (0 ≤ d_i ≤ 10^{12}).

It is guaranteed that the sum of n over all test cases does not exceed 10^5.

Output

For each test case, print "YES" in a single line if there exists a possible array a. Otherwise, print "NO".

You can print letters in any case (upper or lower).

Example

Input


6
2
8 12 8 12
2
7 7 9 11
2
7 11 7 11
1
1 1
4
40 56 48 40 80 56 80 48
6
240 154 210 162 174 154 186 240 174 186 162 210


Output


YES
NO
NO
NO
NO
YES

Note

In the first test case, a=[1,-3,-1,3] is one possible symmetric array that generates the array d=[8,12,8,12].

In the second test case, it can be shown that there is no symmetric array consisting of distinct integers that can generate array d.
/*

https://fb.watch/2_f8UL2Jev/   watch this if you are facing rejections

***********************************************
Don't Copy template it might lead to palagarism
***********************************************
I only Believe on will of fire. 
*******************************
Work so hard, be so good that luck doesn't get a chance to decide the fate of your dreams.
*****************************************************************************************************
If you want to aim high, aim high Don't let that studying and grades consume you Just live life young.
*****************************************************************
If I'm the sun, you're the moon Because when I go up, you go down
*****************************************
I'm working for the day I will surpass you
****************************************

*/ 
  
import java.util.*;
import java.awt.Point;
import java.lang.Math; 
import java.util.Arrays;
import java.util.Scanner;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.OutputStream;
import java.util.Comparator;
import java.math.BigInteger;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.stream.IntStream;
import java.io.IOException;
import java.util.ArrayList;
import java.math.BigInteger;
import java.util.Collections;
import java.util.StringTokenizer;
 
 public class S {
    public static void main(String[] args) throws java.lang.Exception {
        
		FastScanner in=new FastScanner();
	
        int t = in.ni();
        while(t-->0){
          int n = in.ni();
          boolean f=true;
          TreeSet<Long> hs = new TreeSet<>();
          HashMap<Long , Integer> map = new HashMap<>();
          for(int i=0;i<2*n;i++){
              long x = in.nl();
              hs.add(x);
              if(!map.containsKey(x)){
                  map.put(x,1);
              }else{
                  int v  = map.get(x);
                  map.replace(x,v+1);
              }
              if(map.get(x)>2){
                  f=false;
              }
          }
          if(hs.size()!=n || (!f)){
              System.out.println("NO");
          }else{
              long sum=0;
              ArrayList<Long> al = new ArrayList<>(hs);
            //   System.out.println(hs);
              for(int i=n-1;i>=0;i--){
                   long x = al.get(i);
                   x-=sum;
                   if(x>0 && x%(2*(i+1))==0){
                       x/=(2*(i+1));
                       sum+=2*x;
                       al.set(i,x);
                   }else{
                       f=false;
                       System.out.println("NO");
                       break;
                   }
              }
              if(f){
                System.out.println("YES");
              }
          }
        }
    }

    
    static class sortByFirst implements Comparator<Pair>{

        public int compare(Pair a, Pair b){
            return a.x - b.x;
        }
    }
    
    static class Pair {
        int x;
        int y;

        public Pair(int a, int b){
            this.x=a;
            this.y=b;
        }
    }
    

    // static File input = new File("./input0.txt"); 
	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
        }
        String nL() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
		
		int ni() {
			return Integer.parseInt(next());
        }
        long nl() {
			return Long.parseLong(next());
		}
		void print(int a){
		     System.out.println(a);
        }
        void print(long a){
            System.out.println(a);
       }
		String n(){
		     return next();
        }
        
		void ps(String a) {
		        System.out.print(a);
		}
		void pls(String a) {
		        System.out.println(a);
		}
		int[] ria(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=ni();
			return a;
		}
		void pa(int [] a) {
			for (int i=0; i<a.length; i++)
		        System.out.print(a[i]+" ");
		}
	
		
	     void pla(int [] a) {
			for (int i=0; i<a.length; i++)
		        System.out.println(a[i]);
		}
		
	}
 
	

    	
 
    public int factorial(int n) {
            int fact = 1;
            int i = 1;
           while(i <= n) {
             fact *= i;
             i++;
           }
            return fact;
    }
    
    static int max= 1000000;
    static boolean prime[] = new boolean[max+1]; 
    static void sieveOfEratosthenes(int n) { 
         
        for(int i=0;i<n;i++) 
            prime[i] = true; 
        for(int p = 2; p*p <=n; p++) { 
            if(prime[p] == true) { 
                for(int i = p*p; i <= n; i += p) 
                    prime[i] = false; 
            } 
        } 

        return ;
    } 
    

    public static long gcd(long x,long y)
    {
    	if(x%y==0)
    		return y;
    	else
    		return gcd(y,x%y);
    }
    public static int gcd(int x,int y)
    {
    	if(x%y==0)
    		return y;
    	else 
    		return gcd(y,x%y);
    }
    public static int abs(int a,int b)
    {
    	return (int)Math.abs(a-b);
    }
    public static long abs(long a,long b)
    {
    	return (long)Math.abs(a-b);
    }
    public static int max(int a,int b)
    {
    	if(a>b)
    		return a;
    	else
    		return b;
    }
    public static int min(int a,int b)
    {
    	if(a>b)
    		return b;
    	else 
    		return a;
    }
    public static long max(long a,long b)
    {
    	if(a>b)
    		return a;
    	else
    		return b;
    }
    public static long min(long a,long b)
    {
    	if(a>b)
    		return b;
    	else 
    		return a;
    }
     
     
    public static long pow(long n,long p,long m)
    {
    	 long  result = 1;
    	  if(p==0)
    	    return 1;
    	if (p==1)
    	    return n;
    	while(p!=0)
    	{
    	    if(p%2==1)
    	        result *= n;
    	    if(result>=m)
    	    result%=m;
    	    p >>=1;
    	    n*=n;
    	    if(n>=m)
    	    n%=m;
    	}
    	return result;
    }
    public static long pow(long n,long p)
    {
    	long  result = 1;
    	  if(p==0)
    	    return 1;
    	if (p==1)
    	    return n;
    	while(p!=0)
    	{
    	    if(p%2==1)
    	        result *= n;	    
    	    p >>=1;
    	    n*=n;	    
    	}
    	return result;
     
    }
     
    static long sort(int a[]){  
         int n=a.length;
    	int b[]=new int[n];	
    	return mergeSort(a,b,0,n-1);
         
    }
     
    static long mergeSort(int a[],int b[],long left,long right){
         long c=0;
         if(left<right){   
          long mid=left+(right-left)/2;
    	 c= mergeSort(a,b,left,mid);
    	 c+=mergeSort(a,b,mid+1,right);
    	 c+=merge(a,b,left,mid+1,right); 
         }	
    	return c;	 
    }
    static long merge(int a[],int  b[],long left,long mid,long right){
         long c=0;int i=(int)left;int j=(int)mid; int k=(int)left;
         while(i<=(int)mid-1&&j<=(int)right){ 
              if(a[i]<=a[j]){
                   b[k++]=a[i++]; 
              }
              else{ 
                   b[k++]=a[j++];c+=mid-i;
              }
         }
         
         while (i <= (int)mid - 1)   
                 b[k++] = a[i++]; 
         while (j <= (int)right)
                 b[k++] = a[j++];
         for (i=(int)left; i <= (int)right; i++) 
    	        a[i] = b[i];
    	        return c; 
         }
         
      static class InputReader extends BufferedReader {
        public InputReader(InputStream st) {
            super(new InputStreamReader(st));
        }
 
        public String readLine() {
            try {
                return super.readLine();
            } catch (IOException e) {
                return null;
            }
        }
 
        private int readByte() {
            try {
                return read();
            } catch (IOException e) {
                throw new RuntimeException();
            }
        }
 
        public int ni() {
            int num = 0, b;
            boolean minus = false;
            while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
            if (b == '-') {
                minus = true;
                b = readByte();
            }
 
            while (true) {
                if (b >= '0' && b <= '9') {
                    num = num * 10 + (b - '0');
                } else {
                    return minus ? -num : num;
                }
                b = readByte();
            }
        }


       
 
      
 
    } 
     
  } 