C. Nezzar and Symmetric Arraytime limit per test2 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputLong time ago there was a symmetric array a_1,a_2,\ldots,a_{2n} consisting of 2n distinct integers. Array a_1,a_2,\ldots,a_{2n} is called symmetric if for each integer 1 \le i \le 2n, there exists an integer 1 \le j \le 2n such that a_i = -a_j.For each integer 1 \le i \le 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 = \sum_{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.InputThe first line contains a single integer t (1 \le t \le 10^5) — the number of test cases. The first line of each test case contains a single integer n (1 \le n \le 10^5).The second line of each test case contains 2n integers d_1, d_2, \ldots, d_{2n} (0 \le d_i \le 10^{12}).It is guaranteed that the sum of n over all test cases does not exceed 10^5.OutputFor 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).ExampleInput
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
NoteIn 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.
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

YES NO NO NO NO YES 
['implementation', 'math', 'sortings', '*1700']