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- ///UVA 11347 idea: prime power factorization && number of div;
- #include <bits/stdc++.h>
- using namespace std;
- #define ll long long
- #define test int t; cin>>t; for(int cs=1;cs<=t;cs++)
- #define inf 1e18
- vector<ll>prime;
- map<ll,ll>fre;
- void fact(ll n)
- {
- if(n%2==0)
- {
- if(fre[2]==0) prime.push_back(2);
- while(n%2==0)
- {
- fre[2]++;
- n/=2;
- }
- }
- for(ll i=3; i*i<=n; i+=2)
- {
- if(n%i==0)
- {
- if(fre[i]==0) prime.push_back(i);
- while(n%i==0)
- {
- fre[i]++;
- n/=i;
- }
- }
- }
- if(n>1)
- {
- if(fre[n]==0) prime.push_back(n);
- fre[n]++;
- }
- }
- int main()
- {
- ios_base::sync_with_stdio(0);
- cin.tie(0);
- cout.tie(0);
- test
- {
- ll n=0,m,i,j,k=0,l=0,ans=1;
- string a;
- cin>>a;
- for(i=0; i<a.size(); i++)
- {
- if(a[i]=='!') l++;
- else
- {
- n*=10;
- n+=(a[i]-'0');
- }
- }
- prime.clear();
- fre.clear();
- for(i=n; i>1; i-=l)
- {
- fact(i);
- }
- for(i=0; i<prime.size(); i++)
- {
- ans*=(fre[prime[i]]+1);
- if(ans> inf)
- {
- k=1;
- break;
- }
- }
- cout<<"Case "<<cs<<": ";
- if(k) cout<<"Infinity"<<endl;
- else cout<<ans<<endl;
- }
- return 0;
- }
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