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>
n=int(input())
h=list(map(int,input().split()))
check,ans,skip=[0]*300001,0,-1
for i in range(n):
    ans+=h[i]//2
    if h[i]%2==1:
        check[i-1]=min(check[i-1],h[i]-(check[i-1]%2+1)%2)
        if i>0 and check[i-1]%2==0:
            check[i]=check[i-1]+1
        elif i>0 and check[i-1]%2==1:
            check[i]=check[i-1]-1
            ans+=1
        if i==0:
            check[0]=1
    else:
        if check[i-1]==0:
            continue
        check[i-1]=min(check[i-1],h[i]-check[i-1]%2)
        if i>0 and check[i-1]%2==1:
            check[i]=check[i-1]+1
        elif i>0 and check[i-1]%2==0:
            check[i]=check[i-1]-1
print(ans)