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>
# 20200118 19:26 ~ 19:47 ~ 20:20

n = int(input())
arr = list(map(int, input().split()))

ans_1 = 0
ans_2 = 0

for i in range(n):
    if i%2 == 1:
        ans_1+=int(arr[i]/2) + arr[i]%2
        ans_2+=int(arr[i]/2)
    else:
        ans_1+=int(arr[i]/2)
        ans_2+=int(arr[i]/2) + arr[i]%2

print(min(ans_1, ans_2))