#include "hack.h"
#include <vector>
#include<bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define pb push_back
#define ll long long
#define ld long double
const int N=1e6+10;
vector<int>dvs[N+5];
int hack(){
for(int i=1;i<=N;i++) dvs[i].clear();
for(int i=1;i<=N;i++) for(int j=i;j<=N;j+=i) dvs[j].pb(i);
int x=0;
for(int i=N;i>=1&&x==0;i--){
if(collisions({1,i})==1){
x=i-1;
}
}
int res=x;
for(auto i:dvs[x]){
if(collisions({1,i+1})==1) res=min(res,i);
}
return res;
}
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