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())
A = list(map(int, input().split()))

prev_odd = []
ans = 0
for i in range(N):
    if A[i] % 2 == 0:
        ans += A[i] // 2
    else:
        if prev_odd:
            if (i - prev_odd[-1]) % 2 == 1:
                ans += 1
                prev_odd.pop()
            else:
                prev_odd.append(i)
        else:
            prev_odd.append(i)
        ans += A[i] // 2

print(ans)
