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.
#include<bits/stdc++.h>
#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cmath>
#define ll long long
using namespace std;
ll a[200005];
ll p[100005];
int main()
{
	ll t;
	cin>>t;
	while(t--)
	{
		ll n;
		cin>>n;
		for(int i=0;i<2*n;i++)
		{
			cin>>a[i];
		}
		sort(a,a + 2 * n);
		ll m = 2 * n;
		ll cnt = 0;
		bool flag = 1;
		ll sum=0;
		for(int i = 2 * n-1;i >= 0;i = i - 2,m = m - 2)
		{
			if(a[i] != a[i-1])
			{	
				cout<<"NO"<<endl;
				flag = 0;
				break;
			}
		//	for (int i = 1; i <= 100; i ++) {
			//			int r = a - d * i;
			//			if (r >= 0 && r % 10 == 0){
			//				 flag = true;
			//			}
			//		}
			a[i] = a[i] - 2 * sum;
			if(a[i]%m!=0)
			{
				cout<<"NO"<<endl;
				flag = 0;
				break;
			}
			else
			{
				long long tmp=a[i] / m;
				if(cnt != 0)
				{
					if(tmp >= p[cnt-1]||tmp<=0)
					{
						cout<<"NO"<<endl;
						flag =0;
						break;
					}
				}
				p[cnt++]=tmp;
				sum+=tmp;
			}
		}
		if(flag != 0)
		{
			cout<<"YES"<<endl;
		}
	}
	return 0;
}
 	 	  	       	    	  	   					