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-----
aab

-----Sample Output-----
1
1

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'def Z_algorithm(S):\n    l=len(S)\n    A=[0]*l\n    A[0]=l\n    i=1; j=0\n    while i<l:\n        while i+j<l and S[j]==S[i+j]:\n            j+=1\n        if not j:\n            i+=1\n            continue\n        A[i]=j\n        k=1\n        while l-i>k<j-A[k]:\n            A[i+k]=A[k]\n            k+=1\n        i+=k; j-=k\n    return A\n\ndef jugde(W):\n    Z=Z_algorithm(W)\n    l=len(W)\n    B=[True]*l\n    for p in range(1,l):\n        if not B[p-1]:\n            continue\n        k=2\n        while (k-1)*p<=Z[p]:\n            B[k*p-1]=False\n            k+=1\n    return B\n\ndef solve(W):\n    n=len(W)\n    if len(set(W))==1:\n        print(n)\n        print(1)\n        return\n    G=jugde(W)\n    W.reverse()\n    G_rev=jugde(W)\n    if G[-1]:\n        print(1)\n        print(1)\n        return\n    print(2)\n    cnt=0\n    for i in range(n-1):\n        cnt+=G[i] and G_rev[-(i+2)]\n    print(cnt)\n    return\n\nsolve(list(input()))'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13253