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 math
 
YES = 'YES'
NO = 'NO'
MOD = 1000000007
#a = [0]*n
#m = [[0] * m] * n 
 
def input_int():
    return int(input())
 
def input_list():
    return input().split(' ')
 
def input_list_int():
    return list(map(int, input_list()))


def solve():
    n = input_int()
    a = input_list_int()
    m = []
    cmp = {}
    for i in range(0, 2 * n) :
        if a[i] not in cmp :
            cmp[a[i]] = 0
        cmp[a[i]] += 1
        if cmp[a[i]] == 2 :
            del cmp[a[i]]
            m.append(a[i])
    if len(cmp) > 0 :
        print(NO)
    else :
        m.sort(reverse = True)
        delim = 2 * n
        last = 0
        x = []
        #print(m)
        for i in range(0, n) :
            m[i] -= last
            mul = m[i] / delim
            last += 2 * mul
            x.append(mul)
            delim -= 2
        x.sort()
        has = 1
        for i in range(0, n) :
            if x[i] <= 0 or int(x[i]) != x[i] :
                has = 0
            if i > 0 and x[i] == x[i - 1] :
                has = 0
        #print(x)
        print(YES if has == 1 else NO)
       
            

query_count = input_int()
while query_count:
    query_count -= 1
    solve()