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>
using namespace std;
#define ll long long
#define vll vector<ll>
#define pll pair<ll,ll>
#define forA(i,a,n,x) for(ll i=a;i<n;i+=x)
#define forD(i,a,n,x) for(ll i=n-1;i>=a;i-=x)
#define ranit(it,n) for(auto it:n)
#define testCases ll t;cin>>t;while(t--)
#define mp make_pair
#define pb push_back
#define F first
#define S second
#define mod 1000000007
#define init(a,x) memset(a,x,sizeof(a))

int main()
{
	ios_base::sync_with_stdio(false);	cin.tie(NULL);	cout.tie(NULL);
	testCases
	{
		ll n; cin>>n;
		vll v(2*n); forA(i,0,2*n,1)cin>>v[i];

		sort(v.rbegin(), v.rend());

		//ranit(it,v)cout<<it<<" ";cout<<"\n";

		bool ch=true;
		ll temp=0,p=2*n,past=LLONG_MAX-1;

		forA(i,0,2*n,2)
		{
			if(v[i]!=v[i+1])
			{
				ch=false;
				break;
			}
			else
			{
				if((v[i]-temp)%p==0)
				{
					ll tt = (v[i]-temp)/p;
					if(tt>=past || tt<=0)
					{
						ch=false;
						break;
					}
					past=tt;
					//cout<<tt<<" ";

					temp+=(2*tt);
				}
				else
				{
					ch=false;
					break;
				}
			}
			p-=2;
		}

		if(ch)cout<<"YES\n";
		else cout<<"NO\n";

	}
	return 0;
}