#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using Int = long long; template ostream &operator<<(ostream &os, const pair &a) { return os << "(" << a.first << ", " << a.second << ")"; }; template void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; } template bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; } template bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; } int root(vector &uf, int u) { return (uf[u] < 0) ? u : (uf[u] = root(uf, uf[u])); } bool connect(vector &uf, int u, int v) { u = root(uf, u); v = root(uf, v); if (u == v) return false; if (uf[u] > uf[v]) swap(u, v); uf[u] += uf[v]; uf[v] = u; return true; } int M; vector oks; map, int> cache; int calc(vector fs) { vector uf(M, -1); for (int a = 1; a < M; ++a) if (fs[a]) { for (int u = 0; u < M; ++u) { connect(uf, u, (Int)u * a % M); } } for (int a = 1; a < M; ++a) if (root(uf, 1) == root(uf, a)) { fs[a] = true; } auto it = cache.find(fs); if (it != cache.end()) { return it->second; } set app; set used; for (int a = 1; a < M; ++a) if (oks[a] && !fs[a]) { if (used.insert(root(uf, a)).second) { auto gs = fs; gs[a] = true; const int res = calc(gs); app.insert(res); } } int ret = -1; for (int g = 0; ; ++g) { if (!app.count(g)) { ret = g; break; } } return cache[fs] = ret; } int solve(int m) { M = m; oks.assign(m, false); for (int a = 1; a < m; ++a) { oks[a] = (__gcd(m, a) == 1); } cache.clear(); vector start(m, false); return calc(start); } int main() { /* for (int m = 1; m <= 100; ++m) { cerr << m << ": " << solve(m) << " " << cache.size() << endl; } */ int N; for (; ~scanf("%d", &N); ) { vector A(N); for (int i = 0; i < N; ++i) { scanf("%d", &A[i]); } sort(A.begin(), A.end()); int ans = 0; for (int i = 0, j; i < N; i = j) { for (j = i; j < N && A[i] == A[j]; ++j) {} if ((j - i) % 2 != 0) { ans ^= solve(A[i]); } } puts(ans ? "Y" : "X"); } return 0; }