Suppose we have a sequence of non-negative integers, Namely a₁, a₂ ... a_n. At each time we can choose one term a_i with 0 < i < n and we subtract 1 from both a_i and a_i+1. We wonder whether we can get a sequence of all zeros after several operations.

Input

The first line is the number of test cases T (0 < T ≤ 20).

The first line of each test case is a number N (0 < N ≤ 10000). The next line is N non-negative integers, 0 ≤ a_i ≤ 10⁹.

Output

If it can be modified into all zeros with several operations output “YES” in a single line, otherwise output “NO” instead.

Example

Input:
2
2
1 2
2
2 2

Output:
NO
YES

Explanation

It is clear that [1 2] can be reduced to [0 1] but no further to convert all integers to 0. Hence, the output is NO.

In second case, output is YES as [2 2] can be reduced to [1 1] and then to [0 0] in just two steps.