Recently a top secret mission to Mars has taken place. As a result, scientists managed to obtain some information about the Martian DNA. Now we know that any Martian DNA contains at most *m* different nucleotides, numbered from 1 to *m*. Special characteristics of the Martian DNA prevent some nucleotide pairs from following consecutively in this chain. For example, if the nucleotide 1 and nucleotide 2 can not follow consecutively in the Martian DNA, then the chain of nucleotides [1, 2] is not a valid chain of Martian DNA, but the chain of nucleotides [2, 1] can be a valid chain (if there is no corresponding restriction). The number of nucleotide pairs that can't follow in the DNA chain consecutively, is *k*. 

The needs of gene research required information about the quantity of correct *n*-long chains of the Martian DNA. Your task is to write a program that will calculate this value.
The first line contains three space-separated integers *n*, *m*, *k* (1 ≤ *n* ≤ 10<sup class="upper-index">15</sup>, 1 ≤ *m* ≤ 52, 0 ≤ *k* ≤ *m*<sup class="upper-index">2</sup>).

Next *k* lines contain two characters each, without a space between them, representing a forbidden nucleotide pair. The first character represents the first nucleotide in the forbidden pair, the second character represents the second nucleotide.

The nucleotides with assigned numbers from 1 to 26 are represented by English alphabet letters from "a" to "z" (1 is an "a", 2 is a "b", ..., 26 is a "z"). Nucleotides with assigned numbers from 27 to 52 are represented by English alphabet letters from "A" to "Z" (27 is an "A", 28 is a "B", ..., 52 is a "Z").

It is guaranteed that each forbidden pair occurs at most once in the input. It is guaranteed that nucleotide's numbers in all forbidden pairs cannot be more than *m*. Note that order is important in nucleotide pairs.

Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specifier.
def matrix_multiply(A, B):
    return [[sum(a * b for a, b in zip(row_A, col_B)) for col_B in zip(*B)] for row_A in A]

def matrix_power(matrix, n):
    result = [[1 if i == j else 0 for i in range(len(matrix))] for j in range(len(matrix))]
    base = [row[:] for row in matrix]

    while n > 0:
        if n % 2 == 1:
            result = matrix_multiply(result, base)
        base = matrix_multiply(base, base)
        n //= 2

    return result
n,m,k = map(int,input().split())
l = []
for i in range(k):
    l.append(input())

d = {}

import string

# Using string.ascii_lowercase for lowercase letters and string.ascii_uppercase for uppercase letters
letters = list(string.ascii_lowercase + string.ascii_uppercase)


for i in range(m):
    for j in range(m):
        d[letters[i] + letters[j]] = 1
for y in l:
    d[y] = 0

i = 0
matrix = []
l2 = []
for y in d:
    l2.append(d[y])

matrix = [l2[i:i+m] for i in range(0, m*m, m)]


if n != 1:
    result = matrix_power(matrix,n-1)
  
    s = 0
    for x in result:
        for y in x:
            s+=y 
    print(s)

else:
    print(52)












