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.
//package clipse;


import java.util.*;
import java.util.function.Function;
import java.util.stream.Collectors;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.*;
import java.math.*;


public class dp
{
static int A[];
static long B[];
static int n;
static long dp[][];


static boolean check(long l,int d)
{
	long n=l;
	boolean flag=false;
	while(n!=0)
	{
		if(n%10==d)
		{
			flag=true;
			break;
		}
		n=n/10;
	}
	return flag;
	
	
}




	 public static void main(String[] args)
	    {
		StringBuilder sb=new StringBuilder();
		
		int t=i();
		while(t-->0)
		{
			int n=i();
			
			long A[]=new long[2*n];
			
			
			boolean flag=true;
			HashMap<Long,Integer>h=new HashMap<>();
			for(int i=0;i<2*n;i++) 
			{
				A[i]=l();
				h.put(A[i], h.getOrDefault(A[i],0)+1);
				
			}
			ArrayList<Long>l=new ArrayList<>();
			for(Map.Entry hm:h.entrySet())
			{
				if((long)hm.getKey()%2!=0||(int)hm.getValue()%2!=0)
				{
					sb.append("NO \n");
					flag=false;
					break;
				}
				l.add((long)hm.getKey());
			}
			Collections.sort(l);
			if(flag) 
			{
			
			ArrayList<Long>l2=new ArrayList<>();
			for(int i=0;i<l.size();i++)
			{
				l2.add(l.get(l.size()-i-1));
			}
			HashSet<Long>hs=new HashSet<>();
			
			long pre=0;
			long p=0;
			int f=0;
			n=2*n;
			for(int i=0;i<l2.size();i++)
			{
				if((l2.get(i)-pre)%(n-p)!=0|l2.get(i)<(n-p))
				{
					f=-1;
					break;
				}
				
				
				
				long x=(l2.get(i)-pre)/(n-p);
				if(x<=0)
				{
					f=-1;
					break;
				}
				
				
				//System.out.println(x);
				hs.add(x);
				p+=2;
				pre+=2*x;
				
				
			}
			if(hs.size()!=n/2)
				f=-1;
			
			
			if(f==-1)
				sb.append("NO \n");
			else
				sb.append("YES \n");
			
			
			
			
			}
			
			
			
			
		 }
		System.out.println(sb);
	    }
		 
		 
	    
		 
		 
		 
		 
		 
		 
	    	
	 
	 
	    
	 
	 
//*******************************************PRIME FACTORIZE *****************************************************************************************************//
	 static TreeMap<Integer,Integer> prime(long n)
	 {
		 TreeMap<Integer,Integer>h=new TreeMap<>();
		 long num=n;
		 for(int i=2;i<=Math.sqrt(num);i++)
		 {
			 if(n%i==0)
			 {
				 int nt=0;
				 while(n%i==0) {
					 n=n/i;
					 nt++;
				 }
				 h.put(i, nt);
			 }
		 }
		 if(n!=1)
			 h.put((int)n, 1);
		 return h;
		 
	 }
	 
	
	
//*************CLASS PAIR ***********************************************************************************************************************************************
	    static class pair implements Comparable<pair>
	    {
	        long x;
	        long y;
	        long price;

	        pair(long x, long y,long price) {
	            this.x = x;
	            this.y = x+y;
	            this.price=price;
	        }
	        public int compareTo(pair o)
	        {
	        return (int)(y-o.y);
	        }
			
	    }
//*************CLASS PAIR *****************************************************************************************************************************************************
	
	
	

    static 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);
        }
    }

    static 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();
        }
    }

    static InputReader in = new InputReader(System.in);
    static OutputWriter out = new OutputWriter(System.out);
    static int modulus = (int) 1e7;

    public static int[] sort(int[] a) {
        int n = a.length;
        ArrayList<Integer> l = new ArrayList<>();
        for (int i : a)
            l.add(i);
        Collections.sort(l);
        for (int i = 0; i < l.size(); i++)
            a[i] = l.get(i);
        return a;
    }

    public static long pow(long x, long y) {
        long res = 1;
        while (y > 0) {
            if (y % 2 != 0) {
                res = (res * x) % modulus;
                y--;

            }
            x = (x * x) % modulus;
            y = y / 2;
        }
        return res;
    }
//GCD___+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
    public static long gcd(long x, long y) {
        if (x == 0)
            return y;
        else
            return gcd(y % x, x);
    }
    //****************LOWEST COMMON MULTIPLE   *************************************************************************************************************************************

    public static long lcm(long x, long y) {
        return (x * (y / gcd(x, y)));
    }
//INPUT PATTERN******************************************************************************************************************************************************************
    public static int i() {
        return in.Int();
    }

    public static long l() {
        String s = in.String();
        return Long.parseLong(s);
    }

    public static String s() {
        return in.String();
    }

    public static int[] readArray(int n) {
        int A[] = new int[n];
        for (int i = 0; i < n; i++) {
            A[i] = i();
        }
        return A;
    }

    public static long[] readArray(long n) {
        long A[] = new long[(int) n];
        for (int i = 0; i < n; i++) {
            A[i] = l();
        }
        return A;
    }
	
}






	