Binary Programming

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.

Examples

Input

1101

Output

5

Input

0111101101

Output

26

inputFormat

Input

Input is given from Standard Input in the following format:

T

outputFormat

Output

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

Examples

Input

1101

Output

5

Input

0111101101

Output

26

样例

1101

5