# Complement to 0 - advanced

We can reduce any number to 0 by repeatedly applying a complement operation to it in its binary form:

5 = 101 → 10 → 1 → 0 ⇒ 3 complement operations.

This time you’re asked to calculate the number of operations required to get to 0 for really large bit-strings.

Input

The input contains a single line representing the bit-string

`s`

(1 ≤ |s| ≤ ). Output

The output should contain a single integer - the number of complement operations we need to perform to turn

`s`

into 0. Examples

Input | Output |

111111000111110011100 | 6 |

Explanation

111111000111110011100 → 111000001100011 → 111110011100 → 1100011 → 11100 → 11 → 0

#### Constraints

Time limit: 1 seconds

Memory limit: 512 MB

Output limit: 1 MB