Problem:
 Score : 400 points    Problem Statement We have a board with a 2 \times N grid.
Snuke covered the board with N dominoes without overlaps.
Here, a domino can cover a 1 \times 2 or 2 \times 1 square.  Then, Snuke decided to paint these dominoes using three colors: red, cyan and green.
Two dominoes that are adjacent by side should be painted by different colors.
Here, it is not always necessary to use all three colors.  Find the number of such ways to paint the dominoes, modulo 1000000007 .  The arrangement of the dominoes is given to you as two strings S_1 and S_2 in the following manner:   Each domino is represented by a different English letter (lowercase or uppercase).  The j -th character in S_i represents the domino that occupies the square at the i -th row from the top and j -th column from the left.       Constraints  1 \leq N \leq 52  |S_1| = |S_2| = N  S_1 and S_2 consist of lowercase and uppercase English letters.  S_1 and S_2 represent a valid arrangement of dominoes.         Input Input is given from Standard Input in the following format:  N  S_1  S_2       Output Print the number of such ways to paint the dominoes, modulo 1000000007 .        Sample Input 1 3
aab
ccb      Sample Output 1 6  There are six ways as shown below:        Sample Input 2 1
Z
Z      Sample Output 2 3  Note that it is not always necessary to use all the colors.       Sample Input 3 52
RvvttdWIyyPPQFFZZssffEEkkaSSDKqcibbeYrhAljCCGGJppHHn
RLLwwdWIxxNNQUUXXVVMMooBBaggDKqcimmeYrhAljOOTTJuuzzn      Sample Output 3 958681902

Solution (Python):
p = 10**9+7
N = int(input())
S1 = input().strip()
S2 = input().strip()
cnt = 1
cur = 0
if N>=2 and S1[0]==S1[1]:
    cnt = cnt*6
    cur = 2
else:
    cnt = cnt*3
    cur = 1
while cur<N:
    if cur<N-1 and S1[cur]==S1[cur+1]:
        if S1[cur-1]==S2[cur-1]:
            cnt = (cnt*2)%p
            cur += 2
        else:
            cnt = (cnt*3)%p
            cur += 2
    elif S1[cur-1]==S2[cur-1]:
        cnt = (cnt*2)%p
        cur += 1
    elif cur>=2 and S1[cur-2]==S1[cur-1]:
        cur += 1
print(cnt)

Solution (Python):
MOD = 10**9 + 7
N = int(input())
S = input() + "_"
T = input() + "_"
D = []
i = 0
while i < N:
    if S[i] == S[i+1]:
        D.append(2)
        i += 1
    else:
        D.append(1)
    i += 1

if D[0] == 1:
    ans = 3
else:
    ans = 6
for k in range(1,len(D)):
    if D[k-1] == 1 and D[k] == 2:
        ans *= 2
    elif D[k-1] == 2 and D[k] == 1:
        ans *= 1
    elif D[k-1] == 1 and D[k] == 1:
        ans *= 2
    else:
        ans *= 3
    ans %= MOD
print(ans)

Solution (Python):
N = int(input())
S = input()
T = input()
MOD = 10**9 + 7

isPrevI = S[0] == T[0]

ans = 3 if isPrevI else 6
now = 1 if isPrevI else 2

while now < N:
    isI = S[now] == T[now]

    if isPrevI:
        ans *= 2
    elif not isI:
        ans *= 3
    ans %= MOD
    now += 1 if isI else 2
    isPrevI = isI

print(ans)

Solution (Python):
n = int(input())
s1 = str(input())
s2 = str(input())

mod = 10**9+7
ans = 1
flag = False
for i in range(n):
    if s1[i] == s2[i]:
        if i == 0:
            ans *= 3
        else:
            if flag:
                ans *= 2
            else:
                ans *= 1
        flag = True
    else:
        if i == n-1:
            continue
        else:
            if s1[i] == s1[i+1] and s2[i] == s2[i+1]:
                if i == 0:
                    ans *= 6
                else:
                    if flag:
                        ans *= 2
                    else:
                        ans *= 3
            else:
                continue
        flag = False
    ans %= mod
print(ans)

Solution (Python):
N = int(input())
S = [list(input()) for _ in range(2)]

DIVIDER = 1000000007

pattern = []
for i, Si in enumerate(S[0]):
    if i == 0:
        cnt = 1
    else:
        if Si != Si_prev:
            pattern.append(cnt)
            cnt = 1
        else:
            cnt += 1
    
    Si_prev = Si
else:
    pattern.append(cnt)

for i, n_v in enumerate(pattern):
    if i == 0:
        if n_v == 1:
            ans = 3
        else:
            ans = 6
    else:
        if n_v_prev == 1 and n_v == 1:
            ans = (ans * 2) % DIVIDER
        elif n_v_prev == 1 and n_v == 2:
            ans = (ans * 2) % DIVIDER
        elif n_v_prev == 2 and n_v == 1:
            ans = (ans * 1) % DIVIDER
        else:
            ans = (ans * 3) % DIVIDER
    
    n_v_prev = n_v


print(ans)

Solution (Python):
import sys
input = sys.stdin.readline
from collections import *

N = int(input())
S1 = input()[:-1]
S2 = input()[:-1]
i = 0
ans = 1
MOD = 10**9+7

while i<N:
    if S1[i]==S2[i]:
        if i==0:
            ans *= 3
            ans %= MOD
        else:
            if flag==0:
                ans *= 2
                ans %= MOD
        
        flag = 0
        i += 1
    else:
        if i==0:
            ans *= 6
        else:
            if flag==0:
                ans *= 2
                ans %= MOD
            else:
                ans *= 3
                ans %= MOD
        
        flag = 1
        i += 2

print(ans)

Solution (Python):
import sys

sys.setrecursionlimit(10 ** 9)
MOD = 10 ** 9 + 7

N = int(input())
S1 = list(input())
S2 = list(input())

if S1[0] == S2[0]:
    ans = 3
    flag = True 
    i = 1
else:
    ans = 6
    flag = False
    i = 2
while i < N:
    if S1[i] == S2[i]:
        i += 1
        if flag:
            ans = (ans * 2) % MOD
        else:
            flag = True
    else:
        i += 2
        if flag:
            ans = (ans * 2) % MOD
            flag = False
        else:
            ans = (ans * 3) % MOD
    
print (ans)

Solution (Python):
n=int(input())
t=list(input())
t2=list(input())
cnt=0
ans=1
mod=10**9+7
isdif=False
isend=True
while cnt<n:
    if t[cnt]==t2[cnt]:
        if isend:
            ans*=3
            isend=False
        elif not isdif:
            ans*=2
            ans%=mod
        else:
            pass
        isdif=False
        cnt+=1
    elif t[cnt]!=t2[cnt]:
        if isend:
            ans*=6
            isend=False
        elif isdif:
            ans*=3
            ans%=mod
        else:
            ans*=2
            ans%=mod
        isdif=True
        cnt+=2
print(ans)

Solution (Python):
MOD = int(1e9+7)

N = int(input())
S1 = input()
S2 = input()

pattern = []

i = 0
while i < N:
    if i != N-1 and S1[i] == S1[i+1]:
        pattern.append(2)
        i += 2
    else:
        pattern.append(1)
        i += 1

if pattern[0] == 1:
    ans = 3
else:
    ans = 6

for i in range(1, len(pattern)):
    if pattern[i] == 1:
        if pattern[i-1] == 1:
            ans = ans * 2
        else:
            ans *= 1
    else:
        if pattern[i-1] == 1:
            ans *= 2
        else:
            ans *= 3
    ans %= MOD

print(ans)

Solution (Python):
n = int(input())
s = input()
t = input()
i = 0
if s[0]==t[0]:
    h = True
    r = 3
    i += 1
else:
    r = 6
    i += 2
    h = False
mod = 10**9 +7
while i < n:
    if s[i]==t[i]:
        if h:
            i += 1
            r = (r*2)%mod
        else:
            i += 1
            h = True
    else:
        if h:
            r = (r*2)%mod
            h = False
        else:
            r = (r*3)%mod
        i += 2
print(r)

Solution (Python):






N = int(input())
MOD = 1000000007
if N == 1:
    print(3)
    exit()
S = [list(input()) for _ in range(2)]

ans = 1
i = 0
is_x = None
while i < N:
    if i == 0:
        if S[0][i] == S[1][i]:
            ans *= 3
            i += 1
            is_x = True
        else:
            ans *= 6
            i += 2
            is_x = False
    else:
        if S[0][i] == S[1][i]:
            if is_x:
                ans *= 2
            else:
                ans *= 1
            is_x = True
            i += 1
        else:
            if is_x:
                ans *= 2
            else:
                ans *= 3
            is_x = False
            i += 2
    ans = ans % MOD
print(ans)

Solution (Python):


def LI():
    return list(map(int, input().split()))


N = int(input())
S = [input() for _ in range(2)]

MOD = 10 ** 9 + 7


def main():
    ans, i = (3, 1) if S[0][0] == S[1][0] else (6, 2)
    while i < N:
        if S[0][i] == S[1][i]:
            x = 2 if S[0][i - 1] == S[1][i - 1] else 1
            i += 1
        else:
            x = 2 if S[0][i - 1] == S[1][i - 1] else 3
            i += 2
        ans = ans * x % MOD
    
    print(ans)


if __name__ == "__main__":
    main()

Solution (Python):
n=int(input())
s_=[input() for _ in range(2)]
mod=pow(10,9)+7
s=[1]
for i in range(n-1):
  if s_[0][i]==s_[0][i+1]:
    s[-1]+=1
  else:
    s.append(1)
ans=3*s[0]
for i in range(1,len(s)):
  if s[i-1]==1:
    ans*=2
    ans%=mod
  elif s[i]==2:
    ans*=3
    ans%=mod
print(ans%mod)

Solution (Python):
mod=10**9+7
n=int(input())
S=[list(input()) for _ in range(2)]
A=""

cnt=0
for i in range(n):
    if S[0][i]==S[1][i]:
        A +="A"
    else:
        cnt +=1
        if cnt==2:
            A +="B"
            cnt=0

ans=6 if A[0]=="B" else 3
for i in range(1,len(A)):
    num=A[i-1]+A[i]
    if num=="BA":continue
    elif num=="BB":ans *=3
    else:ans *=2
    ans %=mod

print(ans)

Solution (Python):
n = int(input())
s1 = input()
s2 = input()
mod = 10**9 + 7
ind = []
for i,(_s1,_s2) in enumerate(zip(s1,s2)):
    if _s1 == _s2:
        ind.append(i)

cnt = 0
if len(ind) == 0:
    d = 6
    cnt = 2
    single = False
elif ind[0] == 0:
    d = 3
    single = True
    cnt = 1
else:
    d = 6
    single = False
    cnt = 2
        
while cnt < n:
    if cnt in ind: 
        if single: 
            d *= 2
        else:
            d *= 1
        cnt += 1
        single = True
    else: 
        if single:
            d *= 2
        else:
            d *= 3
        cnt += 2
        single = False
    d %= mod
    
print(d)

"""
"""

Solution (Python):
def main(sample_file = ''):

    """ convenient functions
    
    
    
    
    
    """

    """convenient decorator
    
    
        
        
        
        
        
        
        
        
        
        
    """
    
    
    import sys
    sys.setrecursionlimit(10**7)
    from itertools import accumulate, combinations, permutations, product 
    
    from math import factorial, ceil, floor, sqrt
    def factorize(n):
        """return the factors of the Arg and count of each factor
        
        Args:
            n (long): number to be resolved into factors
        
        Returns:
            list of tuples: factorize(220) returns [(2, 2), (5, 1), (11, 1)]
        """
        fct = []  
        b, e = 2, 0  
        while b * b <= n:
            while n % b == 0:
                n = n // b
                e = e + 1
            if e > 0:
                fct.append((b, e))
            b, e = b + 1, 0
        if n > 1:
            fct.append((n, 1))
        return fct
    def combinations_count(n, r):   
        """Return the number of selecting r pieces of items from n kinds of items.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        
        if n < 0 or r < 0:
            raise Exception('combinations_count(n, r) not defined when n or r is negative')
        if n - r < r: r = n - r
        if r < 0: return 0
        if r == 0: return 1
        if r == 1: return n
        numerator = [n - r + k + 1 for k in range(r)]
        denominator = [k + 1 for k in range(r)]
        for p in range(2,r+1):
            pivot = denominator[p - 1]
            if pivot > 1:
                offset = (n - r) % p
                for k in range(p-1,r,p):
                    numerator[k - offset] /= pivot
                    denominator[k] /= pivot
        result = 1
        for k in range(r):
            if numerator[k] > 1:
                result *= int(numerator[k])
        return result
    def combinations_with_replacement_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items allowing individual elements to be repeated more than once.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        if n < 0 or r < 0:
            raise Exception('combinations_with_replacement_count(n, r) not defined when n or r is negative')
        elif n == 0:
            return 1
        else:
            return combinations_count(n + r - 1, r)
    from bisect import bisect_left, bisect_right
    from collections import deque, Counter, defaultdict 
    from heapq import heapify, heappop, heappush, heappushpop, heapreplace,nlargest,nsmallest 
    from copy import deepcopy, copy 
    import operator
    from operator import itemgetter 
    
    
    from functools import reduce, lru_cache
    def chmin(x, y):
        """change minimum
        if x > y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current minimum value
            y (long): potential minimum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x > y:
            x = y
            return (x, True)
        else:
            return (x, False)
    def chmax(x, y):
        """change maximum
        if x < y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current maximum value
            y (long): potential maximum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x < y:
            x = y
            return (x, True)
        else:
            return (x, False)

    from fractions import gcd 
    def gcds(numbers):
        return reduce(gcd, numbers)
    def lcm(x, y):
        return (x * y) // gcd(x, y)
    def lcms(numbers):
        return reduce(lcm, numbers, 1)
    def make_divisors(n, reversed=False):
        """create list of divisors
        
        Args:
            number (int): number from which list of divisors is created
            reversed (bool, optional): ascending order if False. Defaults to False.
        
        Returns:
            list: list of divisors
        """
        divisors = set()
        for i in range(1, int(n**0.5)+1):
            if n % i == 0:
                divisors.add(i)
                divisors.add(n//i)
        return sorted(list(divisors),reverse=reversed)
    
    
    
    INF = 10 ** 18
    MOD = 10 ** 9 + 7
    AtoZ = list('abcdefghijklmnopqrsruvwxyz')
    modpow = lambda a, n, p = MOD: pow(a, n, p) 
    def modinv(a, p = MOD):
        
        
        return modpow(a, p-2, p)
    def modinv_list(n, p = MOD):
        if n <= 1:
            return [0,1][:n+1]
        else:
            inv_t = [0,1]
            for i in range(2, n+1):
                inv_t += [inv_t[p % i] * (p - int(p / i)) % p]
            return inv_t
    def modfactorial_list(n, p = MOD):
        if n == 0:
            return [1]
        else:
            l = [0] * (n+1)
            tmp = 1
            for i in range(1, n+1):
                tmp = tmp * i % p
                l[i] = tmp
            return l
    def modcomb(n, k, fac_list = [], p = MOD):
        
        
        from math import factorial
        if n < 0 or k < 0 or n < k: return 0
        if n == 0 or k == 0: return 1
        if len(fac_list) <= n:
            a = factorial(n) % p
            b = factorial(k) % p
            c = factorial(n-k) % p
        else:
            a = fac_list[n]
            b = fac_list[k]
            c = fac_list[n-k]
        return (a * modpow(b, p-2, p) * modpow(c, p-2, p)) % p
    def modadd(a, b, p = MOD):
        return (a + b) % MOD
    def modsub(a, b, p = MOD):
        return (a - b) % p
    def modmul(a, b, p = MOD):
        return ((a % p) * (b % p)) % p
    def moddiv(a, b, p = MOD):
        return modmul(a, modpow(b, p-2, p))

    class UnionFindTree:
        """union find tree class
        TODO: fix this description...
        how to use (example):
        >>  uf = UnionFindTree(N) 
        >>  if uf.find_root(a) == uf.find_root(b):
        >>      do something
        >>  else:
        >>      do something
        >>      uf.unite(a, b)
        """
        def __init__(self, N):
            self.root = [-1] * (N+1)
            self.rank   = [0]  * (N+1)
            self.connected_num = [1] * (N+1)
    
        def find_root(self,x):
            root = self.root
            while root[x] != -1:
                x = root[x]
            return x
    
        def unite(self,x,y):
            root = self.root
            rank = self.rank
            connected_num = self.connected_num
            find_root = self.find_root
    
            rx = find_root(x)
            ry = find_root(y)
            if rx != ry:
                if rank[rx] < rank[ry]:
                    root[rx] = ry
                    rx,ry = ry,rx
                else:
                    if rank[rx] == rank[ry]:
                        rank[rx] += 1
                    root[ry] = rx       
                connected_num[rx] += connected_num[ry]

    
    
    
    
    
    
    
    

    def BellmanFord(N, M, ABC, vertex_start, vertex_end, value_if_inf = -1, find_shortest = False):
        """to calculate furthest or shortest length between vertex_start and vertex_end using BellmanFord algorithm
        
        Args:
            N (int): number of vertices
            M (int): number of edges
            ABC (list): [(ai, bi, ci) for _ in range(N)] where i-th edge is directed from vertex ai to vertex bi and the length is ci 
            vertex_start (int): start vertex. usually use 0.
            vertex_end (int): end vertex. usually use N-1.
            value_if_inf (int or string as you like, optional): value you want when the furthest (or shortest) distance is infinite (or -infinite). Defaults to -1.
            find_shortest (bool, optional): choose False to find furthest path. Defaults to False.
        
        Returns:
            int or string: normally int (but can be str if you set value_if_inf to str)
            
        Example:
                N, M, P = R()
                ABC = [R() for _ in range(M)]
                ABC = [(a-1, b-1, c-P) for a, b, c in ABC]
                print(BellmanFord(N, M, ABC, 0, N-1, value_if_inf = 'inf'))

        """

        def make_reachable_list(N, M, ABC, vertex_start, vertex_end):
            reachable_to_direct = defaultdict(list)
            reachable_from_direct = defaultdict(list)
            reachable_from_start = [False] * N
            reachable_to_end = [False] * N
            reachable_from_start[vertex_start] = True
            reachable_to_end[vertex_end] = True
            reachable_from_both_sides = [False] * N
            dfs_from_start = []
            dfs_to_end = []
            for a, b, c in ABC:
                reachable_to_direct[a].append(b)
                reachable_from_direct[b].append(a)
                if a == vertex_start:
                    dfs_from_start.append(b)
                    reachable_from_start[b] = True
                if b == vertex_end:
                    dfs_to_end.append(a)
                    reachable_to_end[a] = True
            while dfs_from_start:
                v = dfs_from_start.pop()
                for i in reachable_to_direct[v]:
                    if not reachable_from_start[i]:
                        reachable_from_start[i] = True
                        dfs_from_start.append(i)
            while dfs_to_end:
                v = dfs_to_end.pop()
                for i in reachable_from_direct[v]:
                    if not reachable_to_end[i]:
                        reachable_to_end[i] = True
                        dfs_to_end.append(i)
            for i in range(N):
                reachable_from_both_sides[i] = reachable_from_start[i] and reachable_to_end[i]
            return reachable_from_both_sides
        
        reachable_from_both_sides = make_reachable_list(N, M, ABC, vertex_start, vertex_end)
        
        if find_shortest:
            dist = [INF for i in range(N)]
        else:
            dist = [-INF for i in range(N)]
        
        dist[vertex_start] = 0
        for i in range(N):
            updated = False
            for a, b, c in ABC:
                if not reachable_from_both_sides[a]:
                    continue
                elif find_shortest:
                    update_condition = dist[a] + c < dist[b]
                else:
                    update_condition = dist[a] + c > dist[b]
                if dist[a] != INF and update_condition:
                    dist[b] = dist[a] + c
                    updated = True
                    if i == N-1:
                        return value_if_inf
            if not updated:
                break
        return dist[vertex_end]

    
    def warshall_floyd(number_vertex, XYD, shift_one_for_vertex=False):
        
        
        
        
        
        d = [[float("inf")]*number_vertex for i in range(number_vertex)]
        for x, y, dist in XYD:
            if shift_one_for_vertex:
                x = x - 1
                y = y - 1
            d[x][y] = dist
            d[y][x] = dist
        for i in range(number_vertex):
            d[i][i] = 0 
        for k in range(number_vertex):
            for i in range(number_vertex):
                for j in range(number_vertex):
                    d[i][j] = min(d[i][j],d[i][k] + d[k][j])
        return d


    """ initialize variables and set inputs
    
        
        
            
            
    
        
        
        
        
        
        
        
    
        
        
        
        
    
        
        
    """

    
    r = lambda: sys.stdin.readline().strip()
    r_int = lambda: int(r())
    r_float = lambda: float(r())
    R = lambda: list(map(int, r().split()))
    R_str = lambda: r().split()
    R_map = lambda: map(int, r().split())
    R_float = lambda: list(map(float, r().split()))
    R_tuple = lambda: tuple(map(int, r().split()))

    """ how to treat input
    
    
    
    
    
    
    
    """

    
    if sample_file:
        sys.stdin = open(sample_file)
        
    
    
    
    N = r_int()
    S1 = r()
    S2 = r()
    i = 0
    ans = 0
    
    if N == 1:
        print(3)
        return
    
    if N == 2:
        if S1[0] == S1[1]:
            print(6)
            return
        else:
            print(6) 
            return
    
    if S1[0] == S1[1]:
        ans = 6
        i = 2
        reset_flag = 0
    else:
        ans = 3
        i = 1
        reset_flag = 1
    while True: 
        
        if i == N:
            print(ans)
            return
        elif i == N-1:
            if reset_flag == 0:
                print(ans)
                return
            else:
                print((ans*2)%1000000007)
                return
        if reset_flag == 0:
            if S1[i] == S1[i+1]:
                ans = (ans*3)%1000000007
                i += 2
                reset_flag = 0
            else:
                ans = ans
                i += 1
                reset_flag = 1
        else:
            if S1[i] == S1[i+1]:
                ans = (ans*2)%1000000007
                i += 2
                reset_flag = 0
            else:
                ans = (ans*2)%1000000007
                i += 1
                reset_flag = 1

    
    
    

    """memo: how to use defaultdict of list
    
    Dic = defaultdict(list)
    
    Dic[x].append(y)
    
    for k, v in Dic.items():
    """
    
    """memo: how to solve binary problems
    
    >>> a = 5
    >>> bin_str_a = format(a, '
    >>> print(bin_str_a)
    0b0101 
    """
    
    """memo: how to solve the problem
    creating simple test/answer
    greed
    simple dp
    graph
    """

if __name__ == '__main__':
    main()