The number of divisor function or d(n) is a very interesting function in number theory. It denotes the number of positive divisors of a particular number. For example d(24) = 8 as 24 has eight divisors 1, 2, 3, 4, 6, 8, 12 and 24. In mathematics factorial of a positive integer number n is written as n! and is defined as below: ∏n i=1 The input file contains at most 101 lines of inputs. Each line contains an integer n (0 < n < 5000001). Input is terminated by a line containing a single zero. This value should not be processed. Output For each line of input produce one line of output. This line contains the modulo 100000007 (108 + 7) of d(AF (n)). Sample Input 1 2 3 4 100 0 Sample Output 1 2 6 18 59417661 n! = 1 × 2 × 3 × · · · × n = Another interesting function AF (n) (Again factorial in short) is defined as: AF (n) = 1! × 2! × 3! × . . . × n! = Given n, your job is to find the value of d(AF (n)). Input i! ∏n i=1 i