String Functions

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