P6366 [ChuanZhi Cup #2 Preliminary] Special Flip

Teacher k is studying the code of a virus program. This code is information consisting of a hexadecimal string of length at most $10^6$ (that is, characters `0` to `9` and `A` to `F`). Now teacher k wants to convert it into a binary $0/1$ string (and at this time, you must ensure that the highest bit is $1$). Then, perform a “flip” operation on this $0/1$ string. For each “flip” operation, teacher k can choose one position in the $0/1$ string, and flip this bit and its two adjacent bits (three bits in total) separately (that is, $0$ becomes $1$, and $1$ becomes $0$). If the chosen position is at the beginning or the end of the sequence, then flip this bit and the existing adjacent bit(s). Teacher k wants to know how to use the minimum number of “flip” steps to turn this $0/1$ string into an all-$0$ string.

A hexadecimal string consisting of `0` to `9` and `A` to `F`.

Output the minimum number of “flip” steps needed to turn it into an all-$0$ string. If it is impossible to turn it into an all-$0$ string no matter what, output `No`.

Explanation of the samples: Hexadecimal `15` corresponds to binary `10101`. By flipping positions $1/3/5$, it can all become $0$. Hexadecimal `FF` corresponds to binary `11111111`. By flipping positions $2/5/8$, it can all become $0$. Hexadecimal `10` corresponds to binary `10000`, and it cannot be turned into all $0$. Translated by ChatGPT 5