#include "hack.h"
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int LIM = 1e9;
int hack(){
int low = 2, high = LIM, ans = 1;
while(low <= high){
int mid = (low + high) >> 1, sqr = sqrt(mid - low + 1);
vector<ll>p;
for(int i = 1; i <= sqr; i++){
p.push_back(i);
}
for(int i = 0; low + sqr * i <= mid; i++){
p.push_back(low + sqr * i);
}
sort(p.begin(), p.end());
p.resize(unique(p.begin(), p.end()) - p.begin());
if(collisions(p) == 0){
low = (ans = mid) + 1;
}
else{
high = mid - 1;
}
}
return ans;
}
