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.

Sample Input 1

aab

Sample Output 1

1
1

Sample Input 2

bcbc

Sample Output 2

2
3

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

Sample Input 3

ddd

Sample Output 3

3
1