#include #define REP_(i, a_, b_, a, b, ...) \ for (int i = (a), END_##i = (b); i < END_##i; ++i) #define REP(i, ...) REP_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__) #define ALL(x) std::begin(x), std::end(x) using i64 = long long; template inline bool chmax(T &a, U b) { return a < b and ((a = std::move(b)), true); } template inline bool chmin(T &a, U b) { return a > b and ((a = std::move(b)), true); } template inline int ssize(const T &a) { return (int) std::size(a); } template std::istream &operator>>(std::istream &is, std::vector &a) { for (auto &x: a) is >> x; return is; } template std::ostream &operator<<(std::ostream &os, const std::pair &a) { return os << "(" << a.first << ", " << a.second << ")"; } template std::ostream &print_seq(const Container &a, std::string_view sep = " ", std::string_view ends = "\n", std::ostream &os = std::cout) { auto b = std::begin(a), e = std::end(a); for (auto it = std::begin(a); it != e; ++it) { if (it != b) os << sep; os << *it; } return os << ends; } template struct is_iterable : std::false_type {}; template struct is_iterable())), decltype(std::end(std::declval()))>> : std::true_type { }; template::value && !std::is_same::value && !std::is_same::value>> std::ostream &operator<<(std::ostream &os, const T &a) { return print_seq(a, ", ", "", (os << "{")) << "}"; } void print() { std::cout << "\n"; } template void print(const T &x) { std::cout << x << "\n"; } template void print(const Head &head, Tail... tail) { std::cout << head << " "; print(tail...); } struct Input { template operator T() const { T x; std::cin >> x; return x; } } in; #ifdef MY_DEBUG #include "debug_dump.hpp" #else #define DUMP(...) #endif using namespace std; const int L = 1'000'005; struct PrimeSieve { std::vector spf; // smallest prime factors table. std::vector primes; explicit PrimeSieve(int n) : spf(n + 1) { // O(n) for (int i = 2; i <= n; ++i) { if (spf[i] == 0) { spf[i] = i; primes.push_back(i); } for (const auto &p: primes) { if (i * p > n or p > spf[i]) break; spf[i * p] = p; } } } inline bool is_prime(int n) const { return spf[n] == n; } auto factorize(int n) const { assert(0 < n and n < int(spf.size())); std::vector> res; while (n > 1) { const int p = spf[n]; int count = 0; do { n /= p; ++count; } while (n % p == 0); res.emplace_back(p, count); } return res; } } sieve(L); // O(d(n)) + sorting std::vector enumerate_divisors( const std::vector> &fac) { std::vector res = {1}; for (auto[p, k]: fac) { int sz = res.size(); for (int i = 0; i < sz; ++i) { i64 pp = 1; for (int j = 0; j < k; ++j) { pp *= p; res.push_back(res[i] * pp); } } } //std::sort(res.begin(), res.end()); return res; } // Disjoint closed intervals [l, r] (mapping l to r). class ClosedIntervalSet : public std::map { private: // If true, automatically merges [l, c] and [c+1, r]. bool merge_adjacent; public: ClosedIntervalSet(bool merge_adjacent = true) : merge_adjacent(merge_adjacent) {} // Returns the interval [l, r] which contains p if available. // Otherwise returns this->end(). std::map::iterator get(i64 p) { auto it = upper_bound(p); if (it == begin() || (--it)->second < p) return end(); return it; } // Inserts interval [l, r] void insert(i64 l, i64 r) { auto itl = upper_bound(l), itr = upper_bound(r + merge_adjacent); if (itl != begin()) { if ((--itl)->second < l - merge_adjacent) ++itl; } if (itl != itr) { l = std::min(l, itl->first); r = std::max(r, std::prev(itr)->second); erase(itl, itr); } (*this)[l] = r; } // Removes interval [l, r] void remove(i64 l, i64 r) { auto itl = upper_bound(l), itr = upper_bound(r); if (itl != begin()) { if ((--itl)->second < l) ++itl; } if (itl == itr) return; i64 tl = std::min(l, itl->first); i64 tr = std::max(r, std::prev(itr)->second); erase(itl, itr); if (tl < l) (*this)[tl] = l - 1; if (r < tr) (*this)[r + 1] = tr; } // Are p and q in the same interval? bool same(i64 p, i64 q) { const auto &it = get(p); return it != end() && it->first <= q && q <= it->second; } i64 mex() { auto it = get(0); if (it == end()) return 0; return it->second + 1; } }; auto main() -> int { ios_base::sync_with_stdio(false), cin.tie(nullptr); const int n = in; vector a(n); cin >> a; int amax = *max_element(ALL(a)); vector g(amax + 1, -1); g[1] = 0; for (int x = 2; x <= amax; ++x) { auto ds = enumerate_divisors(sieve.factorize(x)); ClosedIntervalSet cis; for (auto d: ds) { if (d == x) continue; cis.insert(g[d], g[d]); } g[x] = cis.mex(); } int gall = 0; REP(i, n) { gall ^= g[a[i]]; } print(gall == 0 ? "black" : "white"); }