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