#include "hack.h"
#include "bits/stdc++.h"
using namespace std;
typedef long long ll;
ll lsqrt(ll x){
ll l = 1, r = x;
while (l < r){
ll mid = (l+r)/2;
if (mid * mid <= x) l = mid+1;
else r = mid;
}
return l-1;
}
vector<ll> gen(ll x){
ll v = lsqrt(x);
vector<ll> ans;
for (int i = 1; i < v; i++) ans.push_back(i);
for (int i = v; i <= x; i += v) ans.push_back(i);
ans.push_back(x+1);
return ans;
}
int hack(){
ll l = 2, r = 1e9;
while (l < r){
ll mid = (l+r)/2;
if (collisions(gen(mid)) >= 1) r = mid;
else l = mid + 1;
}
return r;
}
