Problem:
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.

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

Solution in PyPy2 (5.6.0) (judge verdict: Wrong Answer)

import sys
w=list(raw_input())
n=len(w)
per=-1
def good(s):
    m=len(s);z=[0]*m;c=0;g=[True]*m
    for i in range(1,m):
        if i+z[i-c]<c+z[c]:z[i]=z[i-c]
        else:
            j=max(0,c+z[c]-i)
            while i+j<n and s[j]==s[i+j]:j+=1
            z[i]=j;c=i
    for p in range(1,m):
        for k in range(2,z[p]/p+2):g[k*p-1]=False
    return g
for j in range(1,n/2+1):
    if w[:n-j]==w[j:]:per=j;break
if per==-1:print 1;print 1;sys.exit()
if per==1:print n;print 1;sys.exit()
gl=good(w)
w.reverse()
gr=good(w)
cnt=0
for i in range(n-1):
    if gl[i] and gr[n-2-i]:cnt+=1
print 2
print cnt