#include using namespace std; using ll=long long; const ll ILL=2167167167167167167; const int INF=2100000000; #define rep(i,a,b) for (int i=(int)(a);i<(int)(b);i++) #define all(p) p.begin(),p.end() template using _pq = priority_queue, greater>; template int LB(vector &v,T a){return lower_bound(v.begin(),v.end(),a)-v.begin();} template int UB(vector &v,T a){return upper_bound(v.begin(),v.end(),a)-v.begin();} template bool chmin(T &a,T b){if(b bool chmax(T &a,T b){if(a void So(vector &v) {sort(v.begin(),v.end());} template void Sore(vector &v) {sort(v.begin(),v.end(),[](T x,T y){return x>y;});} bool yneos(bool a,bool upp=false){if(a){cout<<(upp?"YES\n":"Yes\n");}else{cout<<(upp?"NO\n":"No\n");}return a;} template void vec_out(vector &p,int ty=0){ if(ty==2){cout<<'{';for(int i=0;i<(int)p.size();i++){if(i){cout<<",";}cout<<'"'< T vec_min(vector &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmin(ans,x);return ans;} template T vec_max(vector &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmax(ans,x);return ans;} template T vec_sum(vector &a){T ans=T(0);for(auto &x:a) ans+=x;return ans;} int pop_count(long long a){int res=0;while(a){res+=(a&1),a>>=1;}return res;} template T square(T a){return a * a;} #include int op(int a, int b){ return min(a, b); } int e(){ return INF; } bool f(int x){ return x > 1; } void solve(); // POP'N ROLL MUSIC / TOMOO int main() { ios::sync_with_stdio(false); cin.tie(nullptr); int t = 1; // cin >> t; rep(i, 0, t) solve(); } void solve(){ int N; cin >> N; vector A(N); rep(i, 0, N) cin >> A[i]; int X = 0; vector C(N); int Z = 0; auto calc = [&](auto self, int L, int R) -> void { // cout << L << " " << R << endl; // assert(Z++ < 5); if (L == R) return; int sz; auto calc_sub = [&](auto self2, int l, int r, atcoder::segtree &seg, vector> &inv) -> void { /*if (L == 0 && R == N) { cout << "# " << l << " " << r << endl; rep(i, 0, sz) cout << seg.get(i) << " "; cout << endl; vec_out(A); }*/ if (l == r) return; auto tmp = seg.max_right(0); if (tmp == sz) return; X++; int m = inv[tmp][LB(inv[tmp], l)]; if (m - l > r - (m + 1)){ rep(i, m, r){ int v = seg.get(A[i]); if (v == 1) seg.set(A[i], e()); else seg.set(A[i], v - 1); } self2(self2,l, m, seg, inv); self(self, m + 1, r); } else{ rep(i, l, m + 1){ int v = seg.get(A[i]); if (v == 1) seg.set(A[i], e()); else seg.set(A[i], v - 1); } self2(self2, m + 1, r, seg, inv); self(self, l, m); } }; { unordered_map m; rep(i, L, R){ if (!m.count(A[i])) m[A[i]] = m.size(); A[i] = m[A[i]]; } sz = m.size(); } vector> inv(sz); atcoder::segtree seg(sz); rep(i, L, R){ inv[A[i]].push_back(i); } rep(i, 0, sz) seg.set(i, (int)inv[i].size()); calc_sub(calc_sub, L, R, seg, inv); }; calc(calc, 0, N); cout << (X & 1 ? "Alice\n" : "Bob\n"); } /* * まあなんか言っているけど * unique な要素を選んでそこで分割する話になる * ある区間の grundy がどうなるかを考える * unique な要素がない -> 0 * というか一意な気がしてきた * 幾つに分割できるかを考える * unique な要素を選んで再帰できないか? * segtree で解く */