multiplication_table.cpp

#include <bits/stdc++.h>
//Author : ritchie_s
#define for0(i, n) for (int i = 0; i < (int)(n); ++i) // 0 based indexing
#define for1(i, n) for (int i = 1; i <= (int)(n); ++i) // 1 based indexing
// Short hand for usual tokens
#define pb push_back
#define fi first
#define se second
#define all(x) x.begin(), x.end()
#define sp " "
// Shorthand for commonly used types
using namespace std;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef pair<int, int> ii;
typedef long long ll;
typedef unsigned long long ull;
typedef vector<ll> vll;
typedef vector<vll> vvll;
typedef double ld;
// functions
#define MOD 1000000007
ll min(ll a,int b) { if (a<b) return a; return b; }
ll min(int a,ll b) { if (a<b) return a; return b; }
ll max(ll a,int b) { if (a>b) return a; return b; }
ll max(int a,ll b) { if (a>b) return a; return b; }
ll gcd(ll a,ll b) { if (b==0) return a; return gcd(b, a%b); }
ll lcm(ll a,ll b) { return (a/gcd(a,b))*b; }
string to_upper(string a) { for (int i=0;i<(int)a.size();++i) if (a[i]>='a' && a[i]<='z') a[i]-='a'-'A'; return a; }
string to_lower(string a) { for (int i=0;i<(int)a.size();++i) if (a[i]>='A' && a[i]<='Z') a[i]+='a'-'A'; return a; }
bool prime(ll a) { if (a==1) return 0; for (int i=2;i<=round(sqrt(a));++i) if (a%i==0) return 0; return 1; }
// int gcd = __gcd(a,b) , ll LCM = 1LL*a*b/gcd
//solver fn

ll ok(ll mid , ll n){
    ll cnt = 0;
    for(int i = 1; i<=n ; i++){
        cnt += min(mid/i , n);
    }
    return cnt;
}

void solve(){
    ll n;
    cin>>n;
    if(n == 1){
        cout<<1<<endl;
        return;
    }
    ll lo =  0, hi = n*n;
    while(hi-lo > 1){
        ll mid = lo + (hi-lo)/2;
        ll count = ok(mid , n);
        // if(count == (n*n + 1)/2){
        //     cout<<mid<<endl;
        //     return;
        // }
        if(count >= (n*n + 1)/2){
            hi = mid;
        }
        else{
            lo = mid;
        }
    } 
    cout<<hi<<endl;
}
int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.precision(10);
    cout << fixed;
    solve();
    return 0;
}