#include "hack.h"
#include <bits/stdc++.h>
using namespace std;
bool check(int mid){
vector<long long>X(mid);
iota(X.begin(), X.end(), 1);
return collisions(X) >= 1;
}
int hack(){
int L = 2, R = 1'000'000;
while(L<=R){
int mid = (L+R) / 2;
if (check(mid)){
R = mid - 1;
}else{
L = mid + 1;
}
}
return R + 1;
}
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