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.
import java.util.*;

public class C {
    public static void main(String[] args) {
        Scanner scn = new Scanner(System.in);
        int cases = scn.nextInt();
        while (cases-- > 0) {
            int n = scn.nextInt();
            Map<Long, Integer> map = new HashMap<>();
            for (int i = 0; i < 2 * n; i++) {
                long nr = scn.nextLong();
                int count = 0;
                if (map.containsKey(nr)) count = map.get(nr);
                count++;
                map.put(nr, count);

            }
            List<Long> positive = new ArrayList<>(n);

            boolean solved = true;
            for (int i : map.values()) {
                solved &= (i % 2 == 0);
            }
            for (Map.Entry<Long, Integer> entry : map.entrySet()) {
                long val = entry.getKey();
                int count = entry.getValue();
                count /= 2;
                solved &= (val % 2 == 0);
                while (count-- > 0) positive.add(val / 2);
            }

            long x = 0;
            Collections.sort(positive);
            for (int i = positive.size() - 1; i > -1; i--) {
                if (i == positive.size() - 1) {
                    x = positive.get(i) / (i + 1);
                    solved &= positive.get(i) % (i + 1) == 0;
                    continue;
                }
                long remainder = positive.get(i + 1) - positive.get(i);
                long newX = x - remainder / (i + 1);
                solved &= x != newX && remainder % (i + 1) == 0 && newX > 0;
                x = newX;
            }


            if (solved) System.out.println("YES");
            else System.out.println("NO");


        }

    }


}
