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>
#define fast ios::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define PI 3.14159265358979323846
#define _INF 0x3f3f3f3f3f3f3f3f
#define INF 0x3f3f3f3f
#define MOD 100000007
#define YES cout << "Yes" << endl
#define NO cout << "No" << endl
#define pb push_back
#define JUDGE(x) cout << (x ? "Yes" : "No") << endl
#define Rep(n) for(ll i = 1; i <= n; i++)
#define IN(L, R, A) for (ll i = L; i <= R; i++) cin >> A[i];
#define CF ll Tx; cin >> Tx; while (Tx--)
typedef long long ll;
typedef unsigned int Uint;
typedef unsigned long long Ull;
using namespace std;
const int N = 2e5 + 5;
inline int read(){
    int x = 0, f = 1; char ch = getchar();
    while (!isdigit(ch)) { if (ch == '-') f = -1; ch = getchar(); }
    while (isdigit(ch)) { x = (x << 1) + (x << 3) + (ch ^ 48); ch = getchar(); }
    return x * f;
}

ll arr[N];

bool cmp (ll a, ll b) {return a > b;}

int main() {
    fast;
    CF {
        ll n; cin >> n;
        for (int i = 0; i < 2 * n; i++) cin >> arr[i];
        sort (arr, arr + 2 * n, cmp);
        bool flag = false; ll now = 0;
        for (int i = 0; i < n; i++) {
            if (i > 0 && arr[2 * i] == arr[2 * (i - 1)]) {
                flag = true; break;
            }
            else if (arr[i * 2] == arr[i * 2 + 1]) {
                if (arr[i * 2] - now > 0 && (arr[i * 2] - now) % (2 * (n - i)) == 0)
                    now += (arr[i * 2] - now) / (n - i);
                else {
                    flag = true; break;
                }
            }
            else {
                flag = true; break;
            }
        }
        if (flag) NO; else YES;
    }
}
					 	 		  		   	  	   		 	 		