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 <vector>
#include <iostream>
#include <cstring>
#include <algorithm>
#include <queue>
#include <map>
#include <set>
#include <stack>
#define ll long long
#define chushi(a, b) memset(a, b, sizeof(a))
#define endl "\n"
const double eps = 1e-8;
const ll INF=0x3f3f3f3f;
const int mod = 1e9 + 7;
const int maxn = 3e5 + 5;
const int N=1005;
using namespace std;

map<ll, ll> v;
ll a[maxn];
vector<ll> b;

int main() {

	int ncase;
	cin >> ncase;
	while(ncase--){
		int n;
		cin >> n;
		n <<= 1;
		for(int i = 1; i <= n; i++) cin >> a[i];
		
		for(int i = 1; i <= n; i++){
			int tmp = v[a[i]];
			if(tmp == 0) b.push_back(a[i]);
			v[a[i]]++;
		}
		
		int f = 1, len = b.size();
		for(int i = 0; i < len; i++){
			int tmp = v[b[i]];
			if(tmp != 2){
				f = 0;
				break;
			}
		}
		
		if(len != n / 2) f = 0;
		if(f != 0){
			sort(b.rbegin(), b.rend());
			ll tot = 0, tmp, x;
			for(int i = 0; i < len; i++){
				tmp = b[i] - tot;
				if(tmp % (n-2*i) != 0 || tmp <= 0){
					f = 0;
					break;
				}
				else{
					x = tmp / (n-2*i);
					if(x <= 0){
						f = 0;
						break;
					}
					else{
						tot += 2 * x;
					}
				}
				
			}
		}
		
		if(f) cout << "YES" << endl;
		else cout << "NO" << endl; 
		
		v.clear(); b.clear();
	}
	
	return 0;
}

