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.
for testcase in range(int(input())):
    n=int(input())
    arr=[int(x) for x in input().split()]
    d={}
    for ele in arr:
        if(ele in d):
            d[ele]+=1
        else:
            d[ele]=1
    f=0        
    for ele in d:
        if(d[ele]!=2):
            print("NO")
            f=1
            break
    if(f):
        continue
    s=set(arr)
    if(len(s)!=n):
        print("NO")
    else:
        arr=list(s)
        arr.sort()
        s1=0
        ans=[]
        for i in range(n-1,-1,-1):
            if(i==n-1):
                b=arr[i]
                c=(2*n)
                if(b%c!=0):
                    print("NO")
                    break
                a=b//c
                a=int(a)
                ans.append(a)
                s1+=a
            else:
                b=(arr[i]-(2*s1))
                c=(2*(i+1))
                if(b%c!=0):
                    print("NO")
                    break
                a=b//c
                if(a>ans[-1] or a<=0):
                    print("NO")
                    break
                else:
                    a=int(a)
                    s1+=a
                    ans.append(a)
        else:
            print("YES")
