#ifdef ONLINE_JUDGE #define NDEBUG #endif #if defined(__GNUC__) && !defined(__clang__) // #pragma GCC optimize("O3") // #pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt") #pragma GCC optimize("unroll-loops") #endif // workaround for codeforces g++20 compiler bug #if __cplusplus >= 202002L #define _EXT_CODECVT_SPECIALIZATIONS_H #define _EXT_ENC_FILEBUF_H #endif // #include using namespace std; #if __cplusplus >= 202002L namespace R = ranges; namespace V = views; #endif using i64 = long long; using u64 = unsigned long long; using f64 = double; using uz = size_t; using u32 = uint32_t; using itn = int; template using ve = vector; template using a2 = array; template using HashMap = unordered_map; template using HashSet = unordered_set; template > using PQ = std::priority_queue, C>; template > using miPQ = std::priority_queue, C>; #define mt make_tuple #define mp make_pair #ifdef LOCAL #include "debug_template.cpp" #else #define debug(...) #define debugArr(...) #endif // constexpr array dirs{-1, 0, 1, 0, -1}; // constexpr char nesw[4]{'N', 'E', 'S', 'W'}; // constexpr int M = 1e9 + 7; void cln() { cout << '\n'; } constexpr char ln = '\n'; ve pxor; array dp; int g(int i); int g_impl(int i) { ve s; s.reserve(pxor.size() - i); for (int j = i; j < pxor.size(); ++j) { s.push_back(pxor[j] ^ g(j + 1)); } R::sort(s); int c = 0; for (int i = 0; i < s.size(); ++i) { if (s[i] > c) { return c; } if (s[i] == c) { ++c; } } return c; } int g(int i) { if (i == pxor.size()) { return 0; } auto &memo = dp[i]; if (memo != -1) { return memo; } return memo = g_impl(i); } int main() { #ifndef LOCAL ios::sync_with_stdio(0), cin.tie(0); #endif // dp.fill(-1); int n; cin >> n; pxor.resize(n); cin >> pxor[0]; for (int i = 1; i < n; ++i) { cin >> pxor[i]; pxor[i] ^= pxor[i - 1]; } cout << (g(0) ? "Takahashi" : "Takanashi") << ln; }