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>
# f=open('asdf.txt','r')
# n=int(f.readline())
# array=list(map(int,f.readline().strip().split()))
# from time import *
# import sys
# s = time()
n = int(input())
array = list(map(int, input().split()))
c1, c2 = 0, 0
for i in range(n):
    a = array[i]
    if a % 2 == 0:
        c1 += a // 2
        c2 += a // 2
    else:
        c1 += a // 2
        c2 += a // 2
        if i % 2 == 0:
            c1 += 1
        else:
            c2 += 1
print (min(c1, c2))
# print (time() - s, file=sys.stderr)