Domino for Young

You are given a Young diagram.

Given diagram is a histogram with n columns of lengths a1,a2,…,an (a1≥a2≥…≥an≥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 1×2 or 2×1 rectangle.

The first line of input contain one integer n (1≤n≤300000): the number of columns in the given histogram.

The next line of input contains n integers a1,a2,…,an (1≤ai≤300000,ai≥ai+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.

5
3 2 2 2 1

4

 Note
 
Some of the possible solutions for the example: