[Solution] Difference Operations Codeforces Solution

A. Difference Operations

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

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$a$.

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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.

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