#include "hack.h"
#include <bits/stdc++.h>
using namespace std;
#include <vector>
typedef long long ll;
typedef long long ll;
int hack(){
ll l = 2, r = (ll)1e9 + 5;
ll ans;
while(l <= r){
ll mid = (l + r) >> 1;
vector <ll> v;
ll sq = 1;
ll len = r - l + 1;
while((sq + 1)*(sq + 1) <= len)sq++;
for(ll i = 1 ; i <= sq ; i++)v.push_back(i);
for(ll i = l ; i < mid ; i += sq)v.push_back(i);
v.push_back(mid);
sort(v.begin(), v.end());
v.erase(unique(v.begin(), v.end()), v.end());
ll x = collisions(v);
if(x > 0){
r = mid - 1;
}
else{
ans = mid;
l = mid + 1;
}
}
return ans;
}
