LOJ 1289

#include <bits/stdc++.h>
// #include <iostream>
// #include <cstdio>
// #include <cstdlib>
// #include <algorithm>
// #include <cmath>
// #include <vector>
// #include <set>
// #include <map>
// #include <queue>
// #include <stack>
// #include <ctime>
// #include <cassert>
// #include <complex>
// #include <string>
// #include <cstring>
// #include <bitset>
using namespace std;

// #pragma GCC optimize("Ofast,no-stack-protector")
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
// #pragma GCC optimize("unroll-loops")

#define ll              long long int
#define ui              unsigned int
#define vi              vector< int >
#define vll             vector< ll >

#define sc              scanf
#define pf              printf
#define cspf(i)         pf("Case #%d: ", i)
#define spc             pf(" ")
#define line            pf("\n")

#define ff              first
#define ss              second
#define mp              make_pair
#define pb              push_back
#define ppb             pop_back
#define tp(v,j)         get<j>(v)
#define Log(b,x)        (log(x)/log(b))

#define FOR(i,x,y)      for(int i = int(x); i < int(y); i++)
#define ROF(i,x,y)      for(int i = int(x)-1; i >= int(y); i--)
#define clr(arr,x)      memset(arr, x, sizeof arr)
#define vout(v,sz)      for(int w=0;w<sz;w++){if(w) spc; cout<<v[w];}
#define all(v)          v.begin(), v.end()
#define rall(v)         v.rbegin(), v.rend()
#define unq(v)          sort(all(v)),(v).resize(unique(all(v))-v.begin())
#define fastIO          ios::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr)

#define sc1(x)          sc("%d",&x);
#define sc2(x,y)        sc("%d %d", &x, &y)
#define sc3(x,y,z)      sc("%d %d %d", &x, &y, &z)
#define scl1(x)         sc("%lld",&x);
#define scl2(x,y)       sc("%lld %lld", &x, &y)
#define scf1(x)         sc("%lf",&x);
#define scf2(x,y)       sc("%lf %lf", &x, &y)

#define pf1(x)          pf("%d",x);
#define pf2(x,y)        pf("%d %d", x, y)
#define pfl1(x)         pf("%lld",x);
#define pfl2(x,y)       pf("%lld %lld", x, y)

#define MOD             4294967296LL
#define MaxN            100000000LL
#define inf             0x3f3f3f3f
#define PI              acos(-1.0)  // 3.1415926535897932
#define eps             1e-9

#ifdef ERFANUL007
    #define debug(...) __f(#__VA_ARGS__, __VA_ARGS__)
    template < typename Arg1 >
    void __f(const char* name, Arg1&& arg1){
        cout << name << " = " << arg1 << std::endl;
    }
    template < typename Arg1, typename... Args>
    void __f(const char* names, Arg1&& arg1, Args&&... args){
        const char* comma = strchr(names, ',');
        cout.write(names, comma - names) << " = " << arg1 <<" | ";
        __f(comma+1, args...);
    }
#else
    #define debug(...)
#endif


int N;

vector< ui > prime;
vector< ui > ans;
bitset< MaxN+1 > isPrime;

void precalc(){
    isPrime.set();
    ll i, j;
    ui x;

    for(i=4; i <= MaxN; i += 2) isPrime[i] = 0;
    prime.pb(2);
    ans.pb(2);
    for(i=3; i <= MaxN; i+=2){
        if(isPrime[i]){
            prime.pb(i);
            x = ans.back() * i;
            ans.pb(x);
            for(j=i*i; j <= MaxN; j += (i*2)) isPrime[j] = 0;
        }
    }
    N = prime.size()-1;
    debug(N);
}

int main()
{
    #ifdef ERFANUL007
        clock_t tStart = clock();
        freopen("input.txt", "r", stdin);
        freopen("output.txt", "w", stdout);
    #endif

    precalc();

    int t, ca=0, lo, hi, mid, inx, n, i, occ;
    ui res;
    scanf("%d", &t);

    while(t--){
        scanf("%d", &n);
        res = 1;
        for(i=0; prime[i] * prime[i] <= n; i++){
            occ = Log(prime[i], n) + eps;
            // debug(prime[i], occ);
            while(--occ){
                res *= prime[i];
            }
        }
        // debug(res);
        lo = 0, hi = N;
        while(lo <= hi){
            mid = (lo + hi)/2;
            if(prime[mid] > n) hi = mid-1;
            else{
                lo = mid+1;
                inx = mid;
            }
        }
        res *= ans[inx];
        printf("Case %d: %u\n", ++ca, res);
    }


    #ifdef ERFANUL007
        fprintf(stderr, "\n>> Runtime: %.10fs\n", (double) (clock() - tStart) / CLOCKS_PER_SEC);
    #endif

    return 0;
}