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>
#!/usr/bin/env python3
import sys
input = sys.stdin.readline

n = int(input())
a = [int(item) for item in input().split()] + [0]

black = 0; white = 0
for i, item in enumerate(a):
    if item % 2 == 0:
        black += item // 2
        white += item // 2
    else:
        if i % 2 == 0:
            black += (item + 1) // 2
            white += item // 2
        else:
            white += (item + 1) // 2
            black += item // 2
print(min(black, white))