#include using namespace std; using ll = long long; #define FOR(i, l, r) for(ll i = l; i < r; i++) #define rep(i, n) FOR(i, 0, n) #define FORR(i, l, r) for(ll i = r - 1; i >= l; i--) #define ALL(ar) begin(ar), end(ar) template inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); } template inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); } template istream &operator>>(istream &is, pair &p) { is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const pair &p) { os << p.first << ' ' << p.second; return os; } template istream &operator>>(istream &is, vector &v) { for(T &x : v) is >> x; return is; } template ostream &operator<<(ostream &os, const vector &v) { for(size_t i = 0; i < v.size(); i++) os << (i ? " " : "") << v[i]; return os; } //------------------------------------------------- void solve() { ll n, a, b, c; cin >> n >> a >> b >> c; vector fact(n); vector up(n); fact[0] = 1; FOR(i, 1, n) { fact[i] = fact[i - 1] * i % n; if(fact[i - 1] * i >= n || up[i - 1]) { up[i] = true; } } ll mn = n * a; vector dist(2, vector(n, mn)); dist[0][1] = 0; priority_queue> que; que.emplace(0, 0, 1); while(!que.empty()) { auto [d, x, y] = que.top(); que.pop(); d = -d; if(dist[x][y] < d) continue; if(chmin(dist[x || (y + 1) / n][(y + 1) % n], d + a)) { que.emplace(-d - a, x || (y + 1) / n, (y + 1) % n); } int nx = (x || up[y]); if(chmin(dist[nx][fact[y]], d + c)) { que.emplace(-d - c, nx, fact[y]); } if(x == 1 && chmin(dist[x][0], d + c)) { que.emplace(-d - c, x, 0); } ll cost = b * b; ll ny = y * y % n; nx = (x || y * y >= n); while(true) { if(cost > dist[1][0]) break; if(chmin(dist[nx][ny], d + cost)) { que.emplace(-d - cost, nx, ny); } cost *= b; nx = (nx || ny * y >= n); ny = ny * y % n; } } cout << dist[1][0] << endl; } int main() { int t = 1; // cin >> t; while(t--) solve(); }