import math
from math import *
 
def p12d(int1):
    # based on factorization
    # http://answers.yahoo.com/question/index?qid=20071208133532AAPW5Q7
 
    # i and tri are for advancing the triangular number
    i = 1
    tri = 1
    factors = 1
 
    # loop until there are more than int1 factors
    while factors <= int1:
        factors = 1
 
        ##########
        # Calculate the number of factors that tri has.
 
        prime = 1
        temp = tri
 
        # STOP WHEN PRIME IS BIGGER THAN TRIANGLE:
        while prime <= tri:
 
            # GENERATE THE NEXT PRIME
            prime = prime + 1
            primestat = True            
            rangel = int(sqrt(prime)) + 1
            for item in range(rangel, 1, -1):
                if prime % item == 0:
                    primestat = False
                    break
 
            # IF YOU GET A PRIME
            if primestat == True or prime == 2:
 
                # DIVIDE AS MANY TIMES AS POSSIBLE
                t = 1
                while temp % prime == 0:
                    temp = temp / prime                    
                    t += 1
 
                factors *= t
        ##########
 
        # keep together
        i += 1
        tri += i
 
    # when done, what is the triangle number that meets requirements?
    return tri - i