String Functions

• Time limit: 1.00 s
• Memory limit: 512 MB

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.

Input

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

Output

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

Constraints

• $1 \le n \le 10^6$
  

Example

Input:
abaabca

Output:
0 0 1 2 0 0 1
0 0 1 1 2 0 1