Problem:
Score : 900 points

Problem Statement

Takahashi has an empty string S and a variable x whose initial value is 0.

Also, we have a string T consisting of 0 and 1.

Now, Takahashi will do the operation with the following two steps |T| times.

Insert a 0 or a 1 at any position of S of his choice.

Then, increment x by the sum of the digits in the odd positions (first, third, fifth, ...) of S. For example, if S is 01101, the digits in the odd positions are 0, 1, 1 from left to right, so x is incremented by 2.

Print the maximum possible final value of x in a sequence of operations such that S equals T in the end.

Constraints

1 \leq |T| \leq 2 \times 10^5

T consists of 0 and 1.

Input

Input is given from Standard Input in the following format:

T

Output

Print the maximum possible final value of x in a sequence of operations such that S equals T in the end.

Sample Input 1

1101

Sample Output 1

5

Below is one sequence of operations that maximizes the final value of x to 5.

Insert a 1 at the beginning of S. S becomes 1, and x is incremented by 1.

Insert a 0 to the immediate right of the first character of S. S becomes 10, and x is incremented by 1.

Insert a 1 to the immediate right of the second character of S. S becomes 101, and x is incremented by 2.

Insert a 1 at the beginning of S. S becomes 1101, and x is incremented by 1.

Sample Input 2

0111101101

Sample Output 2

26

Solution in Ruby (2.7.1) (judge verdict: Time Limit Exceeded)

END { load __FILE__ unless $stdin.eof? }

t = gets.chomp.chars.map!(&:to_i)

$list = { [] => 0, [0] => 0, [1] => 1 }

def z(s)
  s.each_slice(2).sum(&:first)
end

def x_max(s)
  $list[s] ||= begin
    Array.new(s.length) { |i| s_sub = s.dup; s_sub.delete_at(i); x_max(s_sub) }.max + z(s)
  end
end

p x_max(t)