Difference Operations

 You are given an array 

a$a$ consisting of n$n$ positive integers.

You are allowed to perform this operation any number of times (possibly, zero):

• choose an index i$i$ (2≤i≤n$2\le i\le n$), and change ai$a_i$ to ai−ai−1$a_i-a_{i-1}$.

Is it possible to make ai=0$a_i=0$ for all 2≤i≤n$2\le i\le n$?

Input

The input consists of multiple test cases. The first line contains a single integer t$t$ (1≤t≤100$1\le t\le 100$)  — the number of test cases. The description of the test cases follows.

The first line contains one integer n$n$ (2≤n≤100$2\le n\le 100$) — the length of array a$a$.

The second line contains n$n$ integers a1,a2,…,an$a_1,a_2,\dots ,a_n$ (1≤ai≤109$1\le a_i\le {10}^9$).

Output

For each test case, print "YES" (without quotes), if it is possible to change ai$a_i$ to 0$0$ for all 2≤i≤n$2\le i\le n$, and "NO" (without quotes) otherwise.

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

Example

input

Copy

4
2
5 10
3
1 2 3
4
1 1 1 1
9
9 9 8 2 4 4 3 5 3

output

Copy

YES
YES
YES
NO

Note

In the first test case, the initial array is [5,10]$[5,10]$. You can perform 2$2$ operations to reach the goal:

1. Choose i=2$i=2$, and the array becomes [5,5]$[5,5]$.
2. Choose i=2$i=2$, and the array becomes [5,0]$[5,0]$.

In the second test case, the initial array is [1,2,3]$[1,2,3]$. You can perform 4$4$ operations to reach the goal:

1. Choose i=3$i=3$, and the array becomes [1,2,1]$[1,2,1]$.
2. Choose i=2$i=2$, and the array becomes [1,1,1]$[1,1,1]$.
3. Choose i=3$i=3$, and the array becomes [1,1,0]$[1,1,0]$.
4. Choose i=2$i=2$, and the array becomes [1,0,0]$[1,0,0]$.

In the third test case, you can choose indices in the order 4$4$, 3$3$, 2$2$.