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: Runtime Error)

long long L,c;t;a['   '];main(i){for(;++i<998;)for(t=i;t<1e6;)a[t+=i]=1;for(;c=1,scanf("%lld",&L)*L;printf("%lld\n",c/2+1))for(i=2;L>1;c*=t-~t,++i)for(t=0;!a[i]&&L%i<1;L/=i)++t;exit(0);}