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
import sys
# t = int(input())
pi = 3.1415
t = 1
for _ in range(t):
    n = int(input())
    a = list(map(int, input().split()))
    wh, bl = 0, 0
    for i in range(len(a)):
        wh, bl = wh+a[i]//2, bl+a[i]//2
        if(a[i] % 2):
            if(i % 2):
                wh += 1
            else:
                bl += 1
    print(min(wh, bl))
