#include "hack.h"
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define pb push_back
#define ff first
#define ss second
#define all(s) s.begin(),s.end()
#define rall(s) s.rbegin(),s.rend()
const ll N=1e9,inf=(ll)1e18;
// collisions
int hack(){
ll lo=2,hi=N;
while(lo<hi){
ll mid=(lo+hi)/2;
ll dif=(mid-lo);
ll s=sqrtl(dif);
vector<ll>v;
v.pb(1);
for(ll i=1;i<s;i++){
v.pb(v.back()+s);
}
v.pb(v.back()+lo);
for(ll i=0;i<s;i++){
v.pb(v.back()+1);
}
for(ll i=0;i<dif-s*s;i++){
v.pb(v.back()+1);
}
if(collisions(v)>0){
hi=mid;
}
else{
lo=mid+1;
}
}
return lo;
}
