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

number_of_columns = int(input())
number_of_cells = 0
figure = input().split()

black_count = 0
white_count = 0

for col_index in range(number_of_columns):
    number_of_cells = int(figure[col_index])
    white_count_col = 0
    black_count_col = 0
    if col_index % 2 == 0:
        white_count_col += math.trunc(number_of_cells/2)
        if number_of_cells % 2 == 1:
            white_count_col += 1
        black_count_col = number_of_cells - white_count_col
    else:
        black_count_col += math.trunc(number_of_cells/2)
        if number_of_cells % 2 == 1:
            black_count_col += 1
        white_count_col = number_of_cells - black_count_col
    white_count += white_count_col
    black_count += black_count_col

print(min(white_count, black_count))

# 1
# 010
# 101
# 010
# 1010