GCD Algo, CF, Pair of Numbers

/**
 *    author:  heWhoCooks
 *    created: 2024-12-27 19:11:27
 **/
#include <bits/stdc++.h>
using namespace std;
mt19937_64 RNG(chrono::steady_clock::now().time_since_epoch().count());
#define NeedForSpeed                  \
    ios_base::sync_with_stdio(false); \
    cin.tie(NULL);                    \
    cout.tie(NULL);
#define int long long
#define all(x) (x).begin(), (x).end()
typedef vector<int> vi;
typedef vector<bool> vb;
typedef vector<vi> vvi;
typedef vector<pair<int, int>> vpi;
#define f first
#define s second
#define pb push_back
#define pf push_front
#define yes cout << "YES" << endl
#define no cout << "NO" << endl
#define endl "\n"
#define M_PI 3.14159265358979323846L
const int mod = 1e9 + 7;
const int INF = 2e18;
int gcd(int a, int b) { return b == 0 ? a : gcd(b, a % b); }
int steps(int a, int b)
{
    if (a == 1)
    {
        return b - 1;
    }
    if (a > b)
    {
        return steps(b, a);
    }
    if (b % a)
    {
        return b / a + steps(b % a, a);
    }
    else
    {
        // not reachable as b%a is 0, means one would be zero
        return 1e9;
    }
}
void solve()
{
    int n;
    cin >> n;
    if (n == 1)
    {
        cout << 0 << endl;
        return;
    }
    int ans = INF;
    // calculating the num steps to reach (a, b) where one number is n
    for (int i = 1; i < n; i++)
    {
        ans = min(ans, steps(i, n));
    }
    cout << ans << endl;
    return;
}

signed main()
{
    NeedForSpeed;
    int t = 1;
    // cin >> t;
    while (t--)
    {
        solve();
    }
    return 0;
}