You are given an array A of length N containing the elements -1 and 1 only. Determine if it is possible to rearrange the array A in such a way that A_{i} is not the geometric mean of A_{i-1} and A_{i+1}, for all i such that 2 ≤ i ≤ N-1.

Y is said to be the geometric mean of X and Z if $Y^{2} = X \cdot Z$.

------ Input Format ------

• The first line contains a single integer T - the number of test cases. Then the test cases follow.
• The first line of each test case contains an integer N - the size of the array A.
• The second line of each test case contains $N space-separated integers A_{1}, A_{2}, \dots, A_{N}$ denoting the array A.

------ Output Format ------

For each test case, output Yes if it is possible to rearrange A in such a way that A_{i} is not the geometric mean of A_{i-1} and A_{i+1}, where 2 ≤ i ≤ N-1. Otherwise output No.

You may print each character of Yes and No in uppercase or lowercase (for example, yes, yEs, YES will be considered identical).

------ Constraints ------

$1 ≤ T ≤ 200$
$3 ≤ N ≤ 1000$
$A_{i} \in \{ -1, 1 \}$

----- Sample Input 1 ------
3
5
1 1 1 -1 -1
3
1 1 1
6
1 -1 -1 -1 -1 1

----- Sample Output 1 ------
Yes
No
Yes

----- explanation 1 ------
Test case 1: We can rearrange the array $A$ to $[1, 1, -1, -1, 1]$. One can see that ${A_{i}}^2 \neq A_{i-1} \cdot A_{i+1}$, for any $2 ≤ i ≤ N-1$.

Test case 2: None of the rearrangements of $A$ satisy the given condition.

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