Pairing for Even Sum

Given a list of integers, determine whether it is possible to divide the list into pairs such that the sum of each pair is even. Two integers form an even sum if both are even or both are odd. In other words, for each pair \( (a, b) \), the condition \( a + b \equiv 0 \pmod{2} \) must hold.

If the list has an odd number of elements, it is not possible to pair all elements, and the answer should be False.

inputFormat

The input is given via stdin. The first line contains an integer n, the number of elements in the list. The second line contains n space-separated integers.

outputFormat

Output a single boolean value (True or False) to stdout, indicating whether the list can be partitioned into pairs with an even sum.

6
2 4 6 8 10 12

True