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 Scala (2.11.7) (judge verdict: Wrong Answer)

import java.util.Scanner

object Main extends App {
  val scanner = new Scanner(System.in)
  val w = scanner.nextLine()

  def uni: String => Boolean = {
    case s if s.length == 0 => true
    case s => s.forall {
      _ == s.head
    }
  }

  def calcKmp(s: String): Seq[Int] = {
    val kmp = new Array[Int](s.length() + 1)
    var j = -1

    kmp(0) = -1

    for (i <- 0 until s.length()) {
      while (j > -1 && s(j) != s(i))
        j = kmp(j)

      j += 1
      kmp(i + 1) = j
    }

    kmp
  }

  def calcPeriod(s: String): Seq[Int] = {
    val kmp = calcKmp(s: String)
    (1 to s.length(), kmp.tail).zipped.map(_ - _)
  }

  def calcGood(s: String): (Int, Int) = {
    if (uni(s)) return (w.length, 1)
    val p = calcPeriod(s).last
    if (p == s.length || s.length % p != 0) return (1, 1)

    val pattern = (calcPeriod(s).init, calcPeriod(s.reverse).reverse.init, 1 until s.length).zipped.count {
      case (l: Int, r: Int, length: Int) =>
        val rLength = s.length - length
        val leftIsGood = length == l || length % l != 0
        val rightIsGood = rLength == r ||  rLength % r != 0
        leftIsGood && rightIsGood
    }
    (2, pattern)

  }

  val (cut, pattern) = calcGood(w)
  println(cut)
  println(pattern)
}