#include <bits/stdc++.h>
using namespace std;
long long collisions(std::vector<long long> x);
bool check(int len){
vector<long long> v;
if (len<=5){
for (int i = 1; i<=len; i++) v.push_back(i);
}
else {
int x = (int)sqrt(len);
for (int i = 1; i<=x; i++) v.push_back(i);
for (int i = x+1; i<=len; i+=x) v.push_back(i);
if (v.back()!=len) v.push_back(len);
}
return collisions(v);
}
int hack(){
int l = 0, r = 1e9+1;
while(r-l>1){
int mid = (l+r)/2;
if (check(mid)) r = mid;
else l = mid;
}
return l;
}
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