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>
''' Hey stalker :) '''
INF = 10**10
def main():
    #print = out.append
    ''' Cook your dish here! '''
    n = get_int()
    li = get_list()
    stk = []
    for i in li:
        if i%2==0 and len(stk)>0:
            stk[-1] += 1
        elif i%2!=0:
            if len(stk)==0: stk.append(0)
            elif stk[-1]%2==0:
                stk.pop()
            else: stk.append(0)
    print((sum(li)-len(stk))//2)


''' Pythonista fLite 1.1 '''
import sys
#from collections import defaultdict, Counter
#from bisect import bisect_left, bisect_right
#from functools import reduce
#import math
input = iter(sys.stdin.buffer.read().decode().splitlines()).__next__
out = []
get_int = lambda: int(input())
get_list = lambda: list(map(int, input().split()))
main()
#[main() for _ in range(int(input()))]
print(*out, sep='\n')
