SOLVE
LATER
Let $$\textrm{pop}(n)$$ is number ones $$n$$ have in binary. For example, $$\textrm{pop}(11) = \textrm{pop}(1011_2) = 3.$$
For integer $$d$$, define
$$$f(d) = \min_{n \geqslant 0} \textrm{pop}(n \oplus (n + d)).$$$
Here $$\oplus$$ denotes binary XOR.
You are given $$d$$ in binary, find $$f(d)$$.
Input Format:
Single line contains binary representation of $$d$$ without leading zeroes.
Output Format:
One integer in decimal numeral system -- $$f(d).$$
Constraints:
$$ 1 \leqslant d < 2 ^ {200,000}.$$
50 points
$$ 1 \leqslant d < 2 ^ {40}.$$
Here $$d = 11_2 = 3.$$