[Solution] Adjacent Sum Parity CodeChef Solution

[Solution] Adjacent Sum Parity CodeChef Solution

Chef has an array A$A$ of length N$N$.

Chef forms a binary array B$B$ of length N$N$ using the parity of the sums of adjacent elements in A$A$. Formally,

• Bi=(Ai+Ai+1)%2$B_i=(A_i+A_{i+1})\mathrm{\%}2$ for 1≤i≤N−1$1\le i\le N-1$
• BN=(AN+A1)%2$B_N=(A_N+A_1)\mathrm{\%}2$

Here x%y$x\mathrm{\%}y$ denotes the remainder obtained when x$x$ is divided by y$y$.

Chef lost the array A$A$ and needs your help. Given array B$B$, determine whether there exits any valid

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 array A$A$ which could have formed B$B$.

Input Format

• The first line contains a single integer T$T$ — the number of test cases. Then the test cases follow.
• The first line of each test case contains an integer N$N$ — the size of the array A$A$.
• The second line of each test case contains N$N$ space-separated integers B1,B2,…,BN$B_1,B_2,\dots ,B_N$ denoting

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•  the array B$B$.

Output Format

For each testcase, output YES if there exists a valid array A$A$, NO otherwise.

You can print any character in any case. For example YES, Yes, yEs are all considered same.

Constraints

• 1≤T≤1000$1\le T\le 1000$
• 2≤N≤105$2\le N\le {10}^5$
• Bi∈{0,1}$B_i\in \{0,1\}$
• The sum of N$N$ over all test cases do not exceed 3⋅105$3\cdot {10}^5$