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>
n = int(input())
data = list(map(int, input().split()))


#data = [11, 10, 9, 8, 7, 6, 5,4,3,2,1]
# data = [3, 2, 2, 2, 1]
# n = len(data)

b, w = 0, 0

for i in range(n):

    n_even = int(data[i]/2)
    n_odd = data[i] - n_even
    if i %2 ==0:
        b += n_even
        w += n_odd
    else:
        b += n_odd
        w += n_even

print(min(b, w))
