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B. Domino for Young

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given a Young diagram.

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

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.

Example

Input

5 3 2 2 2 1

Output

4

Note

Some of the possible solutions for the example:

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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