#include "hack.h"
#include <bits/stdc++.h>
using namespace std;
bool query (int l, int r){
    int gap=sqrt(r-l+1);
    vector<long long> v;
    for (int i=1; i<=gap; ++i)
        v.push_back(i);
    for (int i=max(l+1,gap+1); i<=r; i+=gap)
        v.push_back(i);
    v.push_back(r+1);
    return collisions(v);
}
int hack(){
    int l=1,r=1000000000;
    while (l<r){
        int mid=l+r>>1;
        if (query(l,mid))
            r=mid;
        else
            l=mid+1;
    }
    return l;
}
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