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()))

# total = 0
# last_odd = False
# for a in A:
    # total += a // 2
    # if a % 2 == 1:
        # if last_odd:
            # total += 1
            # last_odd = False
        # else:
            # last_odd = True
    # else:
        # last_odd = False

# print (total)

# checkerboard bound (hopefully it is optimal)
blacks = 0
whites = 0
parity = 0
for a in A:
    if parity:
        whites += a // 2
        blacks += a - a // 2
    else:
        whites += a - a // 2
        blacks += a // 2
    parity ^= 1

print (min(blacks, whites))
