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Difference Operations Solution Codeforces
You are given an array aa consisting of nn positive integers.
You are allowed to perform this operation any number of times (possibly, zero):
- choose an index ii (2≤i≤n2≤i≤n), and change aiai to ai−ai−1ai−ai−1.
Is it possible to make ai=0ai=0 for all 2≤i≤n2≤i≤n?
Input Difference Operations Solution Codeforces
The input consists of multiple test cases. The first line contains a single integer tt (1≤t≤1001≤t≤100) — the number of test cases. The description of the test cases follows.
The first line contains one integer nn (2≤n≤1002≤n≤100) — the length of array aa.
The second line contains nn integers a1,a2,…,ana1,a2,…,an (1≤ai≤1091≤ai≤109).
Output Difference Operations Solution Codeforces
For each test case, print “YES” (without quotes), if it is possible to change aiai to 00 for all 2≤i≤n2≤i≤n, and “NO” (without quotes) otherwise.
You can print letters in any case (upper or lower).
4 2 5 10 3 1 2 3 4 1 1 1 1 9 9 9 8 2 4 4 3 5 3
output Difference Operations Solution Codeforces
Copy
YES YES YES NO
Note Difference Operations Solution Codeforces
In the first test case, the initial array is [5,10][5,10]. You can perform 22 operations to reach the goal:
- Choose i=2i=2, and the array becomes [5,5][5,5].
- Choose i=2i=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 44 operations to reach the goal:
- Choose i=3i=3, and the array becomes [1,2,1][1,2,1].
- Choose i=2i=2, and the array becomes [1,1,1][1,1,1].
- Choose i=3i=3, and the array becomes [1,1,0][1,1,0].
- Choose i=2i=2, and the array becomes [1,0,0][1,0,0].
In the third test case, you can choose indices in the order 44, 33, 22.