You are given a Young diagram.

Given diagram is a histogram with $$$n$$$ columns of lengths $$$a_1, a_2, \ldots, a_n$$$ ($$$a_1 \geq a_2 \geq \ldots \geq a_n \geq 1$$$).

$\text{[math]}$ 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.

Input

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

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

Note

Some of the possible solutions for the example:

$\text{[math]}$ $\text{[math]}$

Domino for Young

Examples