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>
# -*- coding: utf-8 -*-
"""
Created on Sun Dec 22 00:32:52 2019

@author: sj
"""
n=int(input())
a=input().split(" ")
for i in range(n):
    a[i]=int(a[i])
w=a[0]//2
b=a[0]-w
c=1
def no(x):
    if x==1:
        return 0
    return 1
for i in range(1,len(a)):
    if a[i-1]%2==0:
        if a[i]%2==0:
            w+=a[i]//2
            b+=a[i]//2
            c=no(c)
        else:
            if c==1:
                w+=a[i]//2
                b+=a[i]-a[i]//2
            else:
                b+=a[i]//2
                w+=a[i]-a[i]//2
                
    else:
        if a[i]%2==0:
            w+=a[i]//2
            b+=a[i]//2
        else:
            if c==1:
                b+=a[i]//2
                w+=a[i]-a[i]//2
            else:
                w+=a[i]//2
                b+=a[i]-a[i]//2
            c=no(c)
                
         
print(min(b,w))