#include "hack.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using vi = vector<ll>;
int hack(){
int l = 1, r = 1e6;
while(l < r) {
int mid = (l+r)/2;
if(r-l == 1) ++mid;
vi v;
v.push_back(1);
ll cnt = 1;
for(int i=l; i<mid; ++i) {
if(log10(cnt) + log10(i) >= 18) {
v.push_back(cnt+1);
cnt = i;
} else cnt *= i;
}
v.push_back(cnt+1);
int x = collisions(v);
if(x) {
r = mid - 1;
} else l = mid;
}
return r;
}
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