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, stdout

def scal(typ=int):
  return typ(stdin.readline())

def vec(typ=int):
  if isinstance(typ, list):
    inp = stdin.readline().split()
    return [typ[i](inp[i]) for i in range(len(inp))]
  else:
    return list(map(typ, stdin.readline().split()))

n = scal()
A = vec()

i, b, w = 0, 0, 0
for a in A:
  if i:
    w += a - (a // 2)
    b += a // 2
  else:
    w += a // 2
    b += a - (a // 2)
  i = 1 - i

print(min(b, w))
