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>
from sys import stdin, gettrace

if not gettrace():
    def input():
        return next(stdin)[:-1]


def main():
    n = int(input())
    aa = [int(a) for a in input().split()]
    rem = 0
    black = 0
    white = 0
    for i,a in enumerate(aa):
        black += a//2
        white += a//2
        if a%2 == 1:
            if i%2 == 0:
                black +=1
            else:
                white +=1
    print(min(black, white))


if __name__ == "__main__":
    main()