BowWow and the Timetable
Description
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 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 $s$.
Input
The first line contains a single binary number $s$ ($0 \leq s < 2^{100}$) without leading zeroes.
Output
Output a single number — the number of trains which have departed strictly before the time $s$.
Samples
100000000
4
101
2
10100
3
Note
In the first example $100000000_2 = 256_{10}$, missed trains have departed at $1$, $4$, $16$ and $64$.
In the second example $101_2 = 5_{10}$, trains have departed at $1$ and $4$.
The third example is explained in the statements.