Divide Pages CodeChef Solution

Problem

Chef has $N$ books such that the ��ℎith book has ��Ai​ pages. He wants to divide all the books between Alice and Bob such that:

• Both Alice and Bob get at least one book;
• The number of pages allotted to Alice and Bob are either both odd or both even.

Find whether such distribution exists.

Input Format

• The first line of input will contain a single integer $T$, denoting the number of test cases.
• Each test case consists of multiple lines of input.
  • The first line of each test case contains a single integer $N$ — the number of books.
  • The next line contains $N$ space-separated integers, where the ��ℎith integer denotes the number of pages in the ��ℎith book.

Output Format

For each test case, output on a new line, YES, if a valid distribution exists. Otherwise, print NO.

You can print each character in uppercase or lowercase. For example, NO, no, No, and nO, are all considered the same.

Constraints

Sample 1:

3
3
2 4 6
4
1 1 2 3
6
3 1 1 1 1 1

YES
NO
YES

Explanation:

Test case $1$: Consider the distribution where Alice gets books $1$ and $3$, and Bob gets the book $2$. Thus, the number of pages allotted to Alice is $2+6=8$, and the number of pages allotted to Bob is $4$.
Thus, both Alice and Bob have even number of pages allotted to them.

Test case $2$: It can be proven that there exists no valid distribution.

Test case $3$: Consider the distribution where Alice gets the books $1,2,$ and $3$, and Bob gets the books $4,5,$ and $6$. Thus, the number of pages allotted to Alice is $3+1+1=5$, and the number of pages allotted to Bob is $1+1+1=3$.
Thus, both Alice and Bob have odd number of pages allotted to them.