You are given a Young diagram. 

Given diagram is a histogram with n columns of lengths a_1, a_2, …, a_n (a_1 ≥ a_2 ≥ … ≥ a_n ≥ 1).

<image> 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.

Input

The first line of input contain one integer n (1 ≤ n ≤ 300 000): the number of columns in the given histogram.

The next line of input contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 300 000, a_i ≥ 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:

<image> <image>
#! /usr/bin/env python
# -*- coding: utf-8 -*-
import re


def slip():
    return re.sub(r'00|11', '', mid)


n = int(input())
nums = list(map(int, input().split()))
mid = ''
for i in nums:
    if i % 2:
        mid += '1'
    else:
        mid += '0'
l = 0
while l != len(mid):
    l = len(mid)
    mid = slip()

print((sum(nums)-mid.count('1'))//2)

