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.

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