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