Score : $900$ points

Problem Statement

Let $x$ be a string of length at least $1$. We will call $x$ a good string, if for any string $y$ and any integer $k (k \geq 2)$, the string obtained by concatenating $k$ copies of $y$ is different from $x$. For example, a, bbc and cdcdc are good strings, while aa, bbbb and cdcdcd are not.

Let $w$ be a string of length at least $1$. For a sequence $F=(\,f_1,\,f_2,\,...,\,f_m)$ consisting of $m$ elements, we will call $F$ a good representation of $w$, if the following conditions are both satisfied:

• For any $i \, (1 \leq i \leq m)$, $f_i$ is a good string.
• The string obtained by concatenating $f_1,\,f_2,\,...,\,f_m$ in this order, is $w$.

For example, when $w=$aabb, there are five good representations of $w$:

• $($aabb$)$
• $($a$,$abb$)$
• $($aab$,$b$)$
• $($a$,$ab$,$b$)$
• $($a$,$a$,$b$,$b$)$

Among the good representations of $w$, the ones with the smallest number of elements are called the best representations of $w$. For example, there are only one best representation of $w=$aabb: $($aabb$)$.

You are given a string $w$. Find the following:

• the number of elements of a best representation of $w$
• the number of the best representations of $w$, modulo $1000000007 \, (=10^9+7)$

(It is guaranteed that a good representation of $w$ always exists.)

Constraints

• $1 \leq |w| \leq 500000 \, (=5 \times 10^5)$
• $w$ consists of lowercase letters (a-z).

Partial Score

• $400$ points will be awarded for passing the test set satisfying $1 \leq |w| \leq 4000$.

Input

The input is given from Standard Input in the following format:

$w$

Output

Print $2$ lines.

• In the first line, print the number of elements of a best representation of $w$.
• In the second line, print the number of the best representations of $w$, modulo $1000000007$.

aab

1
1

bcbc

2
3

• In this case, there are $3$ best representations of $2$ elements:- $($b$,$cbc$)$
  • $($bc$,$bc$)$
  • $($bcb$,$c$)$
• $($b$,$cbc$)$
• $($bc$,$bc$)$
• $($bcb$,$c$)$

ddd

3
1