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 (Python):
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)

Solution (Python):
w=list(input());n=len(w);t=-1
def Z(s):
    m=len(s);z=[0]*m;c=0;f=[1]*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=j+1
            z[i]=j;c=i
    for p in range(1,m):
        for k in range(2,z[p]//p+2):f[k*p-1]=0
    return f
for j in range(1,n//2+1):
    if n%j==0 and w[:n-j]==w[j:]:t=j;break;
if t==-1:print ('1\n1')
elif t==1:print (n);print (1)
else:
    zl=Z(w)
    w.reverse()
    zr=Z(w)
    cnt=0
    for i in range(0,n-1):
        if zl[i] and zr[n-2-i]:cnt=cnt+1
    print(2);print(cnt);

Solution (Python):
w=list(input())
n=len(w)
t=-1
def Z(s):
    m=len(s);z=[0]*m;c=0;f=[1]*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=j+1
            z[i]=j;c=i
    for p in range(1,m):
        for k in range(2,z[p]//p+2):f[k*p-1]=0
    return f
for j in range(1,n//2+1):
    if n%j==0 and w[:n-j]==w[j:]:t=j;break;
if t==-1:print ('1\n1')
elif t==1:print (n);print (1)
else:
    zl=Z(w)
    w.reverse()
    zr=Z(w)
    cnt=0
    for i in range(0,n-1):
        if zl[i] and zr[n-2-i]:cnt=cnt+1
    print(2);print(cnt);

Solution (Python):
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

W = read().rstrip()

N = len(W)

def Z_algorithm(S):
    
    N=len(S)
    arr = [0]*N
    arr[0] = N
    i,j = 1,0
    while i<N:
        while i+j<N and S[j]==S[i+j]:
            j += 1
        arr[i]=j
        if not j:
            i += 1
            continue
        k = 1
        while i+k<N and k+arr[k]<j:
            arr[i+k] = arr[k]
            k += 1
        i += k; j -= k
    return arr

def is_periodic_left(W):
    Z = Z_algorithm(W)
    is_periodic = [False] * N
    for p in range(1,N//2 + 1):
        if is_periodic[p-1]:
            continue
        for i in range(p,N,p):
            if Z[i] >= p:
                is_periodic[p + i - 1] = True
            else:
                break
    return is_periodic

L = is_periodic_left(W)
R = is_periodic_left(W[::-1])[::-1]

if not L[-1]:
    answer = (1,1)
elif len(set(W)) == 1:
    answer = (N,1)
else:
    x = sum(not(x or y) for x,y in zip(L,R[1:]))
    answer = (2,x)
print('\n'.join(map(str,answer)))

Solution (Python):
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

W = read().rstrip()

N = len(W)

def Z_algorithm(S):
    
    N=len(S)
    arr = [0]*N
    arr[0] = N
    i,j = 1,0
    while i<N:
        while i+j<N and S[j]==S[i+j]:
            j += 1
        arr[i]=j
        if not j:
            i += 1
            continue
        k = 1
        while i+k<N and k+arr[k]<j:
            arr[i+k] = arr[k]
            k += 1
        i += k; j -= k
    return arr

def is_periodic_left(W):
    Z = Z_algorithm(W)
    is_periodic = [False] * N
    for p in range(1,N//2 + 1):
        if is_periodic[p-1]:
            continue
        for i in range(p,N,p):
            if Z[i] >= p:
                is_periodic[p + i - 1] = True
            else:
                break
    return is_periodic

L = is_periodic_left(W)
R = is_periodic_left(W[::-1])[::-1]

if not L[-1]:
    answer = (1,1)
elif len(set(W)) == 1:
    answer = (N,1)
else:
    x = sum(not(x or y) for x,y in zip(L,R[1:]))
    answer = (2,x)
print('\n'.join(map(str,answer)))

Solution (Python):
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

W = read().rstrip()

N = len(W)

def Z_algorithm(S):
    
    N=len(S)
    arr = [0]*N
    arr[0] = N
    i,j = 1,0
    while i<N:
        while i+j<N and S[j]==S[i+j]:
            j += 1
        arr[i]=j
        if not j:
            i += 1
            continue
        k = 1
        while i+k<N and k+arr[k]<j:
            arr[i+k] = arr[k]
            k += 1
        i += k; j -= k
    return arr

def is_periodic_left(W):
    Z = Z_algorithm(W)
    is_periodic = [False] * N
    for p in range(1,N//2 + 10):
        for i in range(p,N,p):
            if Z[i] >= p:
                is_periodic[p + i - 1] = True
            else:
                break
    return is_periodic

L = is_periodic_left(W)
R = is_periodic_left(W[::-1])[::-1]

if not L[-1]:
    answer = (1,1)
elif len(set(W)) == 1:
    answer = (N,1)
else:
    x = sum(not(x or y) for x,y in zip(L,R[1:]))
    answer = (2,x)
print('\n'.join(map(str,answer)))

Solution (Python):
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

W = list(map(int,read().rstrip()))

N = len(W)

def Z_Algorithm(S):
    
    N=len(S)
    arr = [0]*N
    arr[0] = N
    i,j = 1,0
    while i<N:
        while i+j<N and S[j]==S[i+j]:
            j += 1
        arr[i]=j
        if not j:
            i += 1
            continue
        k = 1
        while i+k<N and k+arr[k]<j:
            arr[i+k] = arr[k]
            k += 1
        i += k; j -= k
    return arr

def find_good_substr(W):
    Z = Z_Algorithm(W)
    is_good = [True]*(N+1) 
    for n in range(1,N//2+1):
        
        if not is_good[n]:
            continue
        for i in range(n+n,Z[n]+n+1,n):
            is_good[i] = False
    return is_good

def solve():
    G1 = find_good_substr(W)
    G2 = find_good_substr(W[::-1])[::-1]
    if G1[-1]:
        
        return 1,1
    if len(set(W)) == 1:
        return N,1
    
    x = sum(x and y for x,y in zip(G1[1:-1],G2[1:-1]))
    return 2,x

x,y = solve()
print(x)
print(y)

Solution (Python):
def Z_algorithm(S):
    l=len(S)
    A=[0]*l
    A[0]=l
    i=1; j=0
    while i<l:
        while i+j<l and S[j]==S[i+j]:
            j+=1
        if not j:
            i+=1
            continue
        A[i]=j
        k=1
        while l-i>k<j-A[k]:
            A[i+k]=A[k]
            k+=1
        i+=k; j-=k
    return A

def jugde(W):
    Z=Z_algorithm(W)
    l=len(W)
    B=[True]*l
    for p in range(1,l):
        if not B[p-1]:
            continue
        k=2
        while (k-1)*p<=Z[p]:
            B[k*p-1]=False
            k+=1
    return B

def solve(W):
    n=len(W)
    if len(set(W))==1:
        print(n)
        print(1)
        return
    G=jugde(W)
    W.reverse()
    G_rev=jugde(W)
    if G[-1]:
        print(1)
        print(1)
        return
    print(2)
    cnt=0
    for i in range(n-1):
        cnt+=G[i] and G_rev[-(i+2)]
    print(cnt)
    return

solve(list(input()))

Solution (Python):
from collections import Counter
*W, = map(ord, input())
N = len(W)

C = Counter(W)
if len(C) == 1:
    print(N)
    print(1)
    exit(0)

def z_algo(S):
    A = [0]*N
    i = 1; j = 0
    A[0] = l = len(S)
    while i < l:
        while i+j < l and S[j] == S[i+j]:
            j += 1
        A[i] = j
        if not j:
            i += 1
            continue
        k = 1
        while l-i > k < j - A[k]:
            A[i+k] = A[k]
            k += 1
        i += k; j -= k
    return A

def calc(W):
    Z = z_algo(W)
    G = [0]*N
    for i in range(N):
        G[i] = 1
    for p in range(1, N):
        if not G[p-1]:
            continue
        for k in range(2, Z[p]//p+2):
            G[k*p-1] = 0
    return G
G0 = calc(W)
W.reverse()
G1 = calc(W)

if G0[N-1]:
    print(1)
    print(1)
    exit(0)

print(2)
print(sum(p and q for p, q in zip(G0[:-1], reversed(G1[:-1]))))

Solution (Python):
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 n%j==0:
        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

Solution (Python):
import sys
w=list(raw_input())
n=len(w)
per=-1

def zalg(s):
    z=[0]*n;c=0
    for i in range(1,n):
        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
    z[0] = n
    return z

def good(s):
    g=[True]*n
    z=zalg(s)
    for p in range(1,n):
        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 n%j==0:
        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