#pragma GCC optimize("Ofast")
#pragma GCC optimize("O3,unroll-loops")
#include <bits/stdc++.h>
using namespace std;
#define f0r(i, n) for (auto i = 0; i < (n); ++i)
#define fnr(i, n, k) for (auto i = (n); i < (k); ++i)
#define all(v) (v).begin(), (v).end()
#define pb push_back
#define F first
#define S second
#define ctn(x) cout << x << '\n'
#define forl(a, l) for (auto a : l)
#define ctl(l) for (auto &a : (l)) cout << a << ' '; cout << endl;
#define lb(v, x) (lower_bound(all(v), x) - begin(v))
#define ub(v, x) (upper_bound(all(v), x) - begin(v))
#define pq priority_queue
template <class T>
using V = vector<T>;
using ll = long long;
using vi = V<int>;
using vl = V<ll>;
using pi = pair<int, int>;
using ti = tuple<int, int, int>;
using Adj = V<vi>;
using vvi = V<vi>;
#include "hack.h"
int hack(){
vl A{1};
ll lo = 2, hi = 1e9, ans = 0;
while (lo <= hi) {
ll m = (lo+hi)/2;
ll l = lo, r = m;
ll B = sqrt(r-l+1)+1;
vl A(B);
iota(all(A), 1);
f0r(i, B) A.pb(min(l+i*B, r));
sort(all(A));
A.erase(unique(all(A)), end(A));
if (collisions(A)) {
ans = m;
hi = m-1;
}
else lo = m+1;
}
return ans;
}
