#include "hack.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define all(v) v.begin(), v.end()
bool check(int l, int r) {
int d = r - l;
if (d == 0) return false;
if (d == 1) return collisions({1, l + 1}) > 0;
int b = sqrt(d);
vector<ll> x(b);
iota(all(x), 1ll);
for (int i = l + b; i <= r; i += b) {
x.push_back(i);
}
if (x.back() != r) x.push_back(r);
return collisions(x) > 0;
}
int hack() {
int l = 2, r = 1e9 + 1;
while (l + 1 < r) {
int m = (l + r) / 2;
if (check(l, m)) {
r = m;
}
else {
l = m;
}
}
return l;
}
