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>
import math
N = int(input())
arr = [int(x) for x in input().split()]
tot = 0
hor = 0
for i in range(N):
    if arr[i] >= hor or (hor%2 == arr[i]%2):
        tot += int(math.ceil(min(hor, arr[i])/2))
    else:
        tot += int(math.ceil((min(hor, arr[i])-1)/2))
    if arr[i] >= hor:
        tot += (arr[i]-hor)//2
        if (arr[i] - hor) % 2 == 0:
            hor = max(hor-1, 0)
        else:
            hor += 1
    else:
        hor -= 1
        hor2 = arr[i]
        if hor2%2 != hor%2: hor2 -= 1
        hor = max(hor2, 0)
    #print(tot, hor)
print(tot)

