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>
###############################
# https://codeforces.com/contest/1269/problem/D
# 2021/01/13
# WenhuZhang
################################
from sys import stdin
import collections
import copy

n= int(stdin.readline())
a = list(map(int, stdin.readline().split()))
ans =0
left=[]
for i in range(len(a)):
    # print(ans, left)
    ans += a[i]//2
    if a[i]%2 :
        if not len(left):
            left.append(i)
        elif (i-left[-1])%2:
            # print(i,a)
            left.pop()
            ans+=1
        else:
            left.append(i)
    
print(ans)
        
    
