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>
class Solution(object):
    def solve(self,array):
        b=0
        w=0
        for i in range(0,len(array)):
            if i%2==0:
                tb=array[i]//2
                b+=tb
                w+=array[i]-tb
            else:
                tw=array[i]//2
                w+=tw
                b+=array[i]-tw
        return min(b,w)
        
if __name__=="__main__":
    input_len=int(raw_input().strip())
    array=map(int,raw_input().split(" "))
    T=Solution()
    print T.solve(array)
