#include "hack.h"
#include <bits/stdc++.h>
#define vi vector<int>
#define vll vector<ll>
#define vvi vector<vi>
#define oo 1000000001
#define eb emplace_back
#define pb push_back
#define mpr make_pair
#define ln '\n'
#define ull unsigned long long
#define ll long long
#define all(v) v.begin(), v.end()
#define iospeed ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0)
using namespace std;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
template <typename T> void show(vector<T> &v) {
for (T i : v) {
cout << i << ' ';
}
cout << ln;
}
int hack() {
ll l = 1, r = 1e9;
while (r - l > 2) {
ll mid = (l + r) >> 1;
//cerr << "l r = " << l << ' ' << r << ln;
ll sz = (r - l + 1);
ll sq = sqrt(sz / 2);
vll x;
sq += (sq & 1);
mid += (mid & 1);
for (ll i = 1; i <= sq; i += 2) {
x.eb(i * (1ll << 29));
}
for (ll i = mid; i > l && i > mid / 3; i -= sq) {
x.eb(i * (1ll << 29));
}
ll res = collisions(x);
if (res) {
r = mid;
} else {
l = mid + 1;
}
}
int res = (l + r) >> 1;
while (!collisions({1, res + 1})) res *= 2;
return res;
}
