Reduce Blackboard to One Number

Given a blackboard with \(N\) non-negative integers. In one operation, you can select two integers \(a\) and \(b\) from the blackboard such that \(2\mid(a+b)\) (i.e. \(a+b\) is even), erase them, and write \(\frac{a+b}{2}\) on the blackboard. Note that after each operation, all numbers on the blackboard remain integers.

Your task is to determine whether it is possible to reduce the board to a single number using a sequence of such operations. If it is possible, you must also output one valid sequence of operations.

Operation: Choose two numbers \(a\) and \(b\) with \(a+b\) even, erase them, and append \(\frac{a+b}{2}\) to the board.

inputFormat

The first line contains an integer \(N\) representing the number of integers on the blackboard.

The second line contains \(N\) non-negative integers separated by spaces.

outputFormat

If it is impossible to reduce the board to one number, output NO.

If it is possible, output YES on the first line, then an integer \(K\) (which will be \(N-1\), the number of operations performed), and finally \(K\) lines, each containing two integers representing the two numbers chosen in that operation (in the order they were selected).

sample

2
1 2

NO