127 lines
2.7 KiB
C++
127 lines
2.7 KiB
C++
#include<cstdio>
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#include<cstring>
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#include<cstdlib>
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#include<iostream>
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#include<algorithm>
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#include<cmath>
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#include<vector>
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using namespace std;
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const double eps=1e-8;
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int pr[1231];
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struct A{vector<int> a;double s;}e,te;
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struct P{int p[100],n;double s;}p,da;
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long long mx;
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int pt1(A &e,int n){
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double k=1;
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for(int i=0;i<n;i++){
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k*=pow(pr[i]+0.0,e.a[i]+0.0);
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if(k>p.s*1.00000001)return 0;
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}
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return 1;
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}
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void cf(P &p,int k){
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p.p[p.n]=0;
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for(int i=0;i<p.n;i++)
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p.p[i]*=k;
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for(int i=0;i<p.n;i++)
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p.p[i+1]+=p.p[i]/10,p.p[i]%=10;
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while(p.p[p.n]){
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p.p[p.n+1]=p.p[p.n]/10;
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p.p[p.n]%=10;
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p.n++;
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}
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}
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P qiu(A &a,int n){
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P p;
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p.n=1;
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p.p[0]=1;
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for(int i=0;i<n;i++)
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for(int q=0;q<a.a[i];q++)
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cf(p,pr[i]);
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return p;
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}
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int pt(P a,P b){
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if(a.n!=b.n){
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return a.n<b.n;
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}
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for(int i=a.n;i--;){
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if(a.p[i]!=b.p[i])
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return a.p[i]<b.p[i];
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}
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return 1;
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}
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int s[123],x[123];
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int n;
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long long js(A &e,int n){
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long long da=1;
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for(int i=0;i<n;i++)
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da*=e.a[i]+1;
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return da;
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}
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void dfs(int rt,A& e,long long k){
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if(rt>n)return ;
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if(k>=mx){
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if(!pt1(e,rt))return ;
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if(k>mx||(k==mx&& pt(qiu(e,rt),da))){
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if(!pt(qiu(e,rt),p))return ;
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mx=k;
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da=qiu(e,rt);
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}
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}
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int ss=s[rt];
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if(rt)ss=min(ss,e.a[rt-1]);
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for(int i=ss;i>=x[rt];i--){
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e.a[rt]=i;
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dfs(rt+1,e,k*(e.a[rt]+1));
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}
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}
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int gs(int k){ return 2*(log(pr[n]+0.0)/log(k+0.0))-1;}
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int gx(int k){ return (log(pr[n]+0.0)/log(k+0.0));}
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void qiu(){
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for(n=1;;n++){
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e.a.clear();
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for(int i=0;i<n;i++)
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s[i]=gs(pr[i]),x[i]=gx(pr[i]);
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if(x[0]<3)x[0]=1;
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for(int i=0;i<n;i++)
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e.a.push_back(1);
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if(!pt1(e,n))break;
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}
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if(n<15)
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for(int i=0;i<n;i++)
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x[i]=1;
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e.a.clear();
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for(int i=0;i<n;i++)e.a.push_back(0);
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dfs(0,e,1);
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}
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int main(){
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int ind=0;
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for(int i=2;i<1e3;i++){
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if(pr[i]==0){
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pr[ind++]=i;
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for(int q=i*i;q<1e3;q+=i)
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pr[q]=1;
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}
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}
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string s;
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while(cin>>s){
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if(s=="1"){
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puts("1 1");
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continue;
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}
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mx=-1;
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reverse(s.begin(),s.end());
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p.n=s.size();
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p.s=0;
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for(int i=0;i<s.size();i++){
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p.p[i]=s[i]-'0';
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p.s+=p.p[i]*pow(10.0,i);
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}
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qiu();
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p=da;
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for(int i=p.n;i--;)
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cout<<p.p[i];
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cout<<' '<<mx;cout<<endl;
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}
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}
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