We consider a string of $n$ characters, indexed $1,2,\dots,n$ . Your task is to calculate all values of the following functions:

• $z(i)$ denotes the maximum length of a substring that begins at position $i$ and is a prefix of the string. In addition, $z(1)=0$ .
• $\pi(i)$ denotes the maximum length of a substring that ends at position $i$ , is a prefix of the string, and whose length is at most $i-1$ .

Note that the function $z$ is used in the Z-algorithm, and the function $\pi$ is used in the KMP algorithm.

The only input line has a string of length $n$ . Each character is between a–z.

• $1 \le n \le 10^6$

Print two lines: first the values of the $z$ function, and then the values of the $\pi$ function.