#include "hack.h"
#include <vector>
#include<bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define pb push_back
#define ll long long
#define ld long double
/*const int N=1e6+10;
vector<int>dvs[N+5];*/
const int M=60000;
const ll inf=4e17;
mt19937_64 rng(time(0));
ll Sredi(ll x){
ll res=x;
vector<ll>p;
for(int i=2;i<=sqrt(x);i++){
while(x%i==0){x/=i;p.pb(i);}
}
p.pb(x);
for(auto i:p){
res/=i;
if(collisions({1,res+1})==0) res*=i;
}
return res;
}
vector<ll> Resi(vector<ll>a){
int n=a.size();
vector<ll>b,c;
for(int i=0;i<n;i++){
if(i<=(n-1)/2) b.pb(a[i]);
else c.pb(a[i]);
}
if(collisions(b)) return Resi(b);
if(collisions(c)) return Resi(c);
return a;
}
ll DC(vector<ll>b,vector<ll>c){
if(b.size()==1&&c.size()==1) return abs(b[0]-c[0]);
int l=0,r=b.size()-1,mid=l+r>>1;
int L=0,R=c.size()-1,Mid=L+R>>1;
vector<ll>b1,b2,c1,c2;
for(int i=0;i<=mid;i++) b1.pb(b[i]);
for(int i=mid+1;i<b.size();i++) b2.pb(b[i]);
for(int i=0;i<=Mid;i++) c1.pb(c[i]);
for(int i=Mid+1;i<c.size();i++) c2.pb(c[i]);
vector<ll>temp;
temp=b1;for(auto i:c1) temp.pb(i);
if(collisions(temp)) return DC(b1,c1);
temp=b1;for(auto i:c2) temp.pb(i);
if(collisions(temp)) return DC(b1,c2);
temp=b2;for(auto i:c1) temp.pb(i);
if(collisions(temp)) return DC(b2,c1);
temp=b2;for(auto i:c2) temp.pb(i);
if(collisions(temp)) return DC(b2,c2);
}
int hack(){
/*for(int i=1;i<=N;i++) dvs[i].clear();
for(int i=1;i<=N;i++) for(int j=i;j<=N;j+=i) dvs[j].pb(i);
int x=0;
for(int i=N;i>=1&&x==0;i--){
if(collisions({1,i})==1){
x=i-1;
}
}
int res=x;
for(auto i:dvs[x]){
if(collisions({1,i+1})==1) res=min(res,i);
}
return res;*/
vector<ll>a;
int ct=0;
while(++ct){
a.clear();
for(int i=1;i<=M;i++) a.pb(rng()%inf+1);
if(collisions(a)) break;
}
/*for(int i=1;i<=M/3;i++) a.pb(rng()%inf+1);
while(!collisions(a)){
int n=a.size();
for(int i=1;2*i<=n;i++) a.pb(rng()%inf+1);
}*/
a=Resi(a);
int n=a.size();
cerr<<n<<endl;
int Mid=(n-1)/2;
vector<ll>b,c;
for(int i=0;i<=Mid;i++) b.pb(a[i]);
for(int i=Mid+1;i<n;i++) c.pb(a[i]);
ll res=DC(b,c);
/*int l=Mid+1,r=n-1,ind,ind1;
while(l<r){
int mid=l+r>>1;
//printf("%i %i %i\n",l,mid,r);
vector<ll>temp;
for(int i=0;i<=Mid;i++) temp.pb(a[i]);
for(int i=l;i<=mid;i++) temp.pb(a[i]);
if(collisions(temp)) r=mid;
else l=mid+1;
}
ind=l;
ll res=0;
for(int i=0;i<=Mid;i++){
if(collisions({a[i],a[ind]})){res=abs(a[i]-a[ind]);break;}
}*/
//ind1=l;
//res=abs(a[ind]-a[ind1]);
//cerr<<res<<endl;
res=Sredi(res);
return res;
}
