#include "hack.h"
#include <bits/stdc++.h>
using namespace std;
/*
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
typedef tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;
*/
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
template <class T> using PQMax = priority_queue<T>;
template <class T> using PQMin = priority_queue<T, vector<T>, greater<T>>;
template <class T1, class T2>
void maximize(T1 &a, T2 b){
if (b > a) a = b;
}
template <class T1, class T2>
void minimize(T1 &a, T2 b){
if (b < a) a = b;
}
template <class T>
void read(T &number)
{
bool negative = false;
register int c;
number = 0;
c = getchar();
while (c != '-' && !isalnum(c)) c = getchar();
if (c=='-'){
negative = true;
c = getchar();
}
for (; (c>47 && c<58); c=getchar())
number = number *10 + c - 48;
if (negative)
number *= -1;
}
template <class T, class ...Ts>
void read(T &a, Ts& ... args){
read(a);
read(args...);
}
/*
struct Node
{
int node, len;
Node() {node = len = 0;}
Node(int node, int len) {this -> node = node, this -> len = len;}
};
typedef vector<Node> vg;
*/
#define fi first
#define se second
#define FOR(type, i, a, b) for(type i = (a); i <= (b); i++)
#define REV(type, i, b, a) for(type i = (b); i >= (a); i--)
#define testBit(n, bit) (((n) >> (bit)) & 1)
#define flipBit(n, bit) ((n) ^ (1ll << (bit)))
#define cntBit(n) __builtin_popcount(n)
#define cntBitll(n) __builtin_popcountll(n)
#define log2(n) (31 - __builtin_clz(n))
#define log2ll(n) (63 - __builtin_clzll(n))
#define CURRENT_TIMESTAMP chrono::steady_clock::now().time_since_epoch().count()
#define randomize mt19937_64 mt(CURRENT_TIMESTAMP)
randomize;
struct rnd{
inline static ll next(ll n) {return mt() % n;}
inline static ll next(ll l, ll r) {return l + next(r-l+1);}
};
vector<ll> operator + (const vector<ll> a, const vector<ll> b) {
vector<ll> ans(a.size() + b.size());
int ptr = 0;
for (ll i: a) ans[ptr++] = i;
for (ll i: b) ans[ptr++] = i;
return ans;
}
namespace Subtask1{
constexpr int MAX = 1'000'000;
long long collisions[MAX + 1] = {};
void buildCollisions() {
for (int n = 1; n <= MAX; n++) {
int r = MAX % n, q = MAX / n;
collisions[n]
= 1ll * r * (q+1) * q / 2
+ 1ll * (n-r) * q * (q-1) / 2;
}
}
int getBucket(long long number) {
int lo = 1, hi = MAX;
while (lo <= hi) {
int mid = (lo + hi) / 2;
if (collisions[mid] == number)
return mid;
if (collisions[mid] > number)
lo = mid + 1;
else
hi = mid - 1;
}
return 1/0;
}
}
namespace Subtask3{
const int FIRST = 22500;
pair<vector<ll>, vector<ll>> split(vector<ll> arr) {
int mid = int(arr.size()) / 2;
vector<ll> l(arr.begin(), arr.begin() + mid);
vector<ll> r(arr.begin() + mid, arr.end());
return {l, r};
}
pair<ll, ll> find(vector<long long> arr) {
ll d = arr[0];
while (arr.size() > 1) {
auto [a1, a2] = split(arr);
vector<ll> newA = a1;
if (newA[0] != d) newA.push_back(d);
if (collisions(newA)) arr = a1;
else arr = a2;
}
return {d, arr[0]};
}
pair<ll, ll> find(vector<long long> L, vector<long long> R) {
if ((int)L.size() + (int)R.size() == 2) {
vector<long long> all = L;
all.insert(all.end(), R.begin(), R.end());
return {all[0], all[1]};
}
auto [LL, LR] = split(L);
auto [RL, RR] = split(R);
if (collisions(LL + R)) {
return find(R, LL);
}
else {
return find(R, LR);
}
}
bool test(ll d) {
return collisions({1, d + 1}) != 0;
}
ll calD(const ll num) {
ll tmp = num;
vector<ll> primes;
for (ll d = 2; d * d <= tmp; d++) {
if (tmp % d == 0) {
primes.push_back(d);
while (tmp % d == 0) tmp /= d;
}
}
if (tmp > 1) primes.push_back(tmp);
tmp = num;
for (ll p: primes)
while (tmp % p == 0 and test(tmp / p))
tmp /= p;
return tmp;
}
int solve() {
int cnt = 0;
vector<ll> a, b;
for (int i = 0; i < FIRST; i++)
a.push_back(i + 1);
for (int i = 1; i < FIRST; i++) {
ll num = 500'000'000 + i * FIRST;
b.push_back(num);
if (num > 1'000'000'000) break;
}
ll num;
auto [tmp1, tmp2] = find(b);
if (collisions({tmp1, tmp2}))
num = abs(tmp1 - tmp2);
else {
auto [d1, d2] = find(a, b);
num = abs(d1 - d2);
}
ll answer = calD(num);
return answer;
}
}
int hack(){
// Subtask1::buildCollisions();
// std::vector<long long> all(Subtask1::MAX);
// std::iota(all.begin(), all.end(), 1);
// return Subtask1::getBucket(collisions(all));
return Subtask3::solve();
}
