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`).

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.

Examples

Input

aab


Output

1
1


Input

bcbc


Output

2
3


Input

ddd


Output

3
1
import sys
readline = sys.stdin.readline

class Rollinhash:
    def __init__(self, S):
        N = len(S)
        self.mod = 10**9+9
        self.base = 2009          
        self.has = [0]*(N+1)
        self.power = [1]*(N+1)
        for i in range(N):
            s = S[i]
            self.has[i+1] = (self.has[i]*self.base + s)%self.mod
            self.power[i+1] = self.power[i]*self.base%self.mod
 
    def rh(self, i, j):
        return (self.has[j] - self.has[i]*self.power[j-i])%self.mod

MOD = 10**9+7
 
S = list(map(ord, readline().strip()))
N = len(S)
if len(set(S)) == 1:
    print(N)
    print(1)
else:
    Rs = Rollinhash(S)
    
    tabler = [True]*(N+1)
    for d in range(1, 1+N//2):
        r = Rs.rh(0, d)
        for i in range(1, N//d):
            if r != Rs.rh(i*d, (i+1)*d):
                break
            tabler[(i+1)*d] = False
    tablel = [True]*(N+1)
    for d in range(1, 1+N//2):
        r = Rs.rh(N-d, N)
        for i in range(1, N//d):
            if r != Rs.rh(N-(i+1)*d, N-i*d):
                break
            tablel[N-(i+1)*d] = False
    
    if tabler[N]:
        print(1)
        print(1)
    else:
        print(2)
        ans = 0
        for i in range(N+1):
            if tabler[i] and tablel[i]:
                ans += 1
        assert ans > 0, ''
        print(ans)
        