#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) r = mid;
else l = mid + 1;
}
return l;
}
vector<ll> gen(ll l, ll r){
ll len = r - l + 1;
ll v = lsqrt(len);
set<ll> ans;
for (int i = 1; i <= v; i++) ans.insert(i);
for (int i = l+1; i <= r; i += v) ans.insert(i);
ans.insert(r+1);
vector<ll> a;
a.assign(ans.begin(), ans.end());
return a;
}
int hack(){
ll l = 2, r = 1e9;
while (l < r){
ll mid = (l+r)/2;
if (collisions(gen(l, mid)) >= 1) r = mid;
else l = mid + 1;
}
return r;
}
