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

hrz = 0
cnt = 0

for i in range(n):
    nblock = arr[i] - hrz
    cnt += nblock // 2
    cnt += (hrz // 2) + (hrz % 2)
    if i == n-1:
        continue
    if nblock % 2  == 1:
        hrz += 1
    elif hrz > 0:
        hrz -= 1
    if hrz > arr[i+1]:
        if hrz % 2 == arr[i+1] % 2:
            hrz = arr[i+1]
        else:
            hrz = arr[i+1] - 1
print(cnt)