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 Go (1.6) (judge verdict: Wrong Answer)

package main
import "fmt"
const mod int64 = 1000000007
func main() {
  var w string
  fmt.Scan(&w)
  z := z_algorithm(w)
  n := len(w)
  m := 1
  for i:=1;i<n;i++ {
    if i+z[i] == n && n%i == 0 { m = n/i;break }
  }
  fmt.Println(m)
  fmt.Println(comb(int64(n-1),int64(m-1)))
}
func z_algorithm(s string) []int {
  n := len(s)
  z := make([]int,n)
  z[0] = n
  for i,j:=1,0;i<n; {
    for i+j < n && s[j:j+1] == s[i+j:i+j+1] { j++ }
    z[i] = j
    if j == 0 { i++;continue }
    k := 1
    for ;i+k<n&&k+z[k]<j;k++ { z[i+k] = z[k] }
    i,j = i+k,j-k
  }
  return z
}
func comb(n,k int64) int64 {
  if 2*k > n { return comb(n,n-k) }
  if n < 0 || k < 0 { return 0 }
  if n == 0 && k == 0 { return 1 }
  if n == 0 { return 0 }
  num,den := int64(1),int64(1)
  for i:=k;i>0;i-- {
    num = (num*(n+i-k))%mod
    den = (den*i)%mod
  }
  return (num*inv(den))%mod
}
func inv(n int64) int64 {
  a,b := n%mod,mod
  x,y := int64(0),int64(1)
  for b != 0 {
    q := a/b
    a,b = b,a%b
    x,y = y-q*x,x
  }
  for y < 0 { y += mod }
  return y%mod
}