Alex had an array A of length N such that 1≤Ai≤N for all 1≤i≤N. He constructed another binary array B of length N in the following manner: Bi=1 if the frequency of element i in A is odd. Bi=0 if the frequency of element i in A is even. Such an array B is called the parity encoding array of A. For example, if A=[1,1,2,3], then B=[0,1,1,0]. Unfortunately, he completely forgot the array A and vaguely remembers the parity encoding array B. He is now wondering whether there exists any valid array A for which the parity encoding array is B. Can you help himf? Input Format The first line contains a single integer T — the number of test cases. Then the test cases follow. The first line of each test case contains an integer N — the size of the arrays A and B. The second line of each test case contains N space-separated integers B1,B2,…,BN denoting the parity encoding array B. Output Format For each test case, output YES if there exists any valid array A for which the parity encoding array is B. Otherwise, output NO. You may print each character of YES and NO in uppercase or lowercase (for example, yes, yEs, Yes will be considered identical). Constraints 1≤T≤105 1≤N≤105 Bi∈{0,1} Sum of N over all test cases does not exceed 2⋅105.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Input Format

The first line contains a single integer T — the number of test cases. Then the test cases follow.
The first line of each test case contains an integer N — the size of the arrays A and B.
The second line of each test case contains N space-separated integers B1,B2,…,BN denoting the parity encoding array B.

Output Format

For each test case, output YES if there exists any valid array A for which the parity encoding array is B. Otherwise, output NO.

You may print each character of YES and NO in uppercase or lowercase (for example, yes, yEs, Yes will be considered identical).

Constraints

1≤T≤10⁵
1≤N≤10⁵
Bi∈{0,1}
Sum of N over all test cases does not exceed 2⋅10⁵.

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