ProjectEuler#34 Digit factorials

#145 is a curious number, as 1! + 4! + 5! = 1 + 24 + 120 = 145.

#Find the sum of all numbers which are equal to the sum of the factorial of
#their digits.

#Note: as 1! = 1 and 2! = 2 are not sums they are not included.


#A factorion is a natural number that equals the sum of the
#factorials of its decimal digits.
#Upper Bound: 1,854,721
#Source: http://en.wikipedia.org/wiki/Factorion

def fact(n):
    if n == 1 or n == 0:
        return 1
    return n*fact(n-1)

def digitsFacSum(n):
    digitsStr = str(n)
    count = 0
    for i in digitsStr:
        count += fact(int(i))
    return count

limit = 1854721
count = 0
for i in range(3,limit+1):
    if digitsFacSum(i) == i:
        count += i
print count