Problem:
Problem J: No Story

Since I got tired to write long problem statements, I decided to make this problem statement short. For given positive integer L, how many pairs of positive integers a, b (a ≤ b) such that LCM(a, b) = L are there? Here, LCM(a, b) stands for the least common multiple of a and b.

Input

For each dataset, an integer L is given in a line. Input terminates when L = 0.

Output

For each dataset, output the number of pairs of a and b.

Constraints

1 ≤ L ≤ 1012

Sample Input

12
9
2
0

Output for the Sample Input

8
3
2

Solution in C (judge verdict: Wrong Answer)

long long l,i;main(r,x){for(;scanf("%lld",&l),l;printf("%d\n",l>1?3*r:r/2+1))for(i=r=1;++i*i<=l;r*=2*x+1)for(x=0;!(l%i);l/=i)x++;exit(0);}