//chockolateman
#include<bits/stdc++.h>
#include <vector>
#include "hack.h"
using namespace std;
bool done[1000005];
long long memo[1000005];
vector<int> nums;
long long query(long long x)
{
if(done[x])
return memo[x];
done[x] = true;
vector<long long> temp;
temp.push_back(1);
temp.push_back(1+x);
memo[x] = collisions(temp);
return memo[x];
}
int hack(){
memset(done,false,sizeof(done));
memset(memo,0ll,sizeof(memo));
std::vector<long long> temp;
bool broke = false;
int counter = -1;
if(nums.empty())
for(int i = 1 ; i <= 500000 ; i++)
nums.push_back(i);
random_shuffle(nums.begin(),nums.end());
while(!broke)
{
temp.clear();
counter++;
temp.push_back(1);
temp.push_back(1 + nums[counter]);
if(query(nums[counter]))
broke = true;
}
int n = nums[counter];
for(int x = 1 ; x <= n ; x++)
if(n%x==0)
{
temp.clear();
temp.push_back(1);
temp.push_back(1 + x);
if(query(x))
n = x;
}
return n;
}
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