A12824 | BowWow and the Timetable

In the city of Saint Petersburg, a day lasts for $2^{100}$ minutes. From the main station of Saint Petersburg, a train departs after $1$ minute, $4$ minutes, $16$ minutes, and so on; in other words, the train departs at time $4^k$ for each integer $k \geq 0$ . Team BowWow has arrived at the station at the time $s$ and it is trying to count how many trains have they missed; in other words, the number of trains that have departed strictly before time $s$ . For example if $s = 20$ , then they missed trains which have departed at $1$ , $4$ and $16$ . As you are the only one who knows the time, help them!

Note that the number $s$ will be given you in a [binary representation](https://en.wikipedia.org/wiki/Binary_number#Representation) without leading zeroes.

The first line contains a single binary number $s$ ( $0 \leq s < 2^{100}$ ) without leading zeroes.

Output a single number — the number of trains which have departed strictly before the time $s$ .