CF1268B Domino for Young

You are given a Young diagram. Given diagram is a histogram with $ n $ columns of lengths $ a_1, a_2, \ldots, a_n $ ( $ a_1 \geq a_2 \geq \ldots \geq a_n \geq 1 $ ). Young diagram for $ a=[3,2,2,2,1] $ .Your goal is to find the largest number of non-overlapping dominos that you can draw inside of this histogram, a domino is a $ 1 \times 2 $ or $ 2 \times 1 $ rectangle.

The first line of input contain one integer $ n $ ( $ 1 \leq n \leq 300\,000 $ ): the number of columns in the given histogram. The next line of input contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 1 \leq a_i \leq 300\,000, a_i \geq a_{i+1} $ ): the lengths of columns.

Output one integer: the largest number of non-overlapping dominos that you can draw inside of the given Young diagram.

Some of the possible solutions for the example: