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.
__author__ = 'Erfan Sadeqi Azer'

def toInd(c):
    x=ord(c)
    if ord('a')<=x and x<=ord('z'):
        return x-ord('a')
    elif ord('A')<=x and x<=ord('Z'):
        return x-ord('A')+26
    else:
        assert("ERROR")


def emptyMatrix(a,b,value=None,diagonal=False):
    return [[(value if not diagonal or i==j else 0) for i in range(a)] for j in range(b)]


def multiply(A,B,p):
    assert(len(A[0])==len(B))
    C=emptyMatrix(len(A),len(B[0]))
    for i in range(len(A)):
        for j in range(len(B[0])):
            t=0
            for k in range(len(B)):
                t+=A[i][k]*B[k][j]%p
            C[i][j]=t
    return C


def matrixFastPower(M,n,p):
    powers=M
    result=emptyMatrix(len(M),len(M),value=1,diagonal=True)
    while n>0:
        if n%2==1:
            result=multiply(result,powers,p)
        powers=multiply(powers,powers,p)
        n=n>>1
    return result


p=1000000007 #(10**9 + 7)
n,m,k=map(int,input().split())
allowedPairs=emptyMatrix(m,m,1)
for i in range(k):
    pair=input()
    allowedPairs[toInd(pair[0])][toInd(pair[1])]=0


def fastMethod(n,allowedpairs):
    result=matrixFastPower(allowedpairs,n-1,p)
    return sum(map(sum, result))%p

resultMain=fastMethod(n,allowedPairs)
print(resultMain)