codeforces#P1478C. Nezzar and Symmetric Array

Nezzar and Symmetric Array

Description

Long time ago there was a symmetric array a1,a2,,a2na_1,a_2,\ldots,a_{2n} consisting of 2n2n distinct integers. Array a1,a2,,a2na_1,a_2,\ldots,a_{2n} is called symmetric if for each integer 1i2n1 \le i \le 2n, there exists an integer 1j2n1 \le j \le 2n such that ai=aja_i = -a_j.

For each integer 1i2n1 \le i \le 2n, Nezzar wrote down an integer did_i equal to the sum of absolute differences from aia_i to all integers in aa, i. e. di=j=12naiajd_i = \sum_{j = 1}^{2n} {|a_i - a_j|}.

Now a million years has passed and Nezzar can barely remember the array dd and totally forget aa. Nezzar wonders if there exists any symmetric array aa consisting of 2n2n distinct integers that generates the array dd.

The first line contains a single integer tt (1t1051 \le t \le 10^5) — the number of test cases.

The first line of each test case contains a single integer nn (1n1051 \le n \le 10^5).

The second line of each test case contains 2n2n integers d1,d2,,d2nd_1, d_2, \ldots, d_{2n} (0di10120 \le d_i \le 10^{12}).

It is guaranteed that the sum of nn over all test cases does not exceed 10510^5.

For each test case, print "YES" in a single line if there exists a possible array aa. Otherwise, print "NO".

You can print letters in any case (upper or lower).

Input

The first line contains a single integer tt (1t1051 \le t \le 10^5) — the number of test cases.

The first line of each test case contains a single integer nn (1n1051 \le n \le 10^5).

The second line of each test case contains 2n2n integers d1,d2,,d2nd_1, d_2, \ldots, d_{2n} (0di10120 \le d_i \le 10^{12}).

It is guaranteed that the sum of nn over all test cases does not exceed 10510^5.

Output

For each test case, print "YES" in a single line if there exists a possible array aa. Otherwise, print "NO".

You can print letters in any case (upper or lower).

Samples

输入数据 1

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

输出数据 1

YES
NO
NO
NO
NO
YES

Note

In the first test case, a=[1,3,1,3]a=[1,-3,-1,3] is one possible symmetric array that generates the array d=[8,12,8,12]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 dd.