Problem F
LCM Cardinality
Input: Standard Input

Output: Standard Output

Time Limit: 2 Seconds

A pair of numbers has a unique LCM but a single number can be the LCM of more than one possible pairs. For example 12 is the LCMof (1, 12), (2, 12), (3,4) etc. For a given positive integer N, the number of different integer pairs with LCM is equal to N can be called theLCM cardinality of that number N. In this problem your job is to find out the LCM cardinality of a number.

Input

The input file contains at most 101 lines of inputs. Each line contains an integer N (0<N<=2*10⁹). Input is terminated by a line containing a single zero. This line should not be processed.

Output

For each line of input except the last one produce one line of output. This line contains two integers N and C. Here N is the input number and C is its cardinality. These two numbers are separated by a single space.

Sample Input                             Output for Sample Input

2 

12 

24 

101101291 

0 

 1 #include<stdio.h>
 2 #include<string.h>
 3 #include<stdlib.h>
 4 #include<math.h>
 5 #include<iostream>
 6 #include<algorithm>
 7 using namespace std;
 8 int gcd(int x,int y)
 9 {
10     if(y==0)return x;
11     return gcd(y,x%y);
12 }
13 int lcm(int x,int y)
14 {
15     return x/gcd(x,y)*y;
16 }
17 long long c[500];
18 int main()
19 {
20     int n,nu,i,j,size,ans;
21     while(scanf("%d",&n),n)
22     {
23         ans=nu=0;
24         size=sqrt(n+0.5);
25         for(i=1; i<=size; i++)
26         {
27             if(n%i==0)
28             {
29                 c[nu++]=i;
30                 if(i*i!=n)
31                     c[nu++]=n/i;
32             }
33         }
34         for(i=0; i<nu; i++)
35         {
36             for(j=i; j<nu; j++)
37                 if(lcm(c[i],c[j])==n)ans++;
38         }
39         cout<<n<<" "<<ans<<endl;
40     }
41 }