import std.conv, std.functional, std.range, std.stdio, std.string; import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, std.regex, std.typecons; import core.bitop; class EOFException : Throwable { this() { super("EOF"); } } string[] tokens; string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; } int readInt() { return readToken.to!int; } long readLong() { return readToken.to!long; } real readReal() { return readToken.to!real; } bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } } bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } } int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; } int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); } int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); } enum E = 32; class Tree { Tree l, r; int e; long sum; this(int e) { this.e = e; } void insert(long a) { if (e == 0) { sum = 1; } else { if (a & 1L << (e - 1)) { if (!r) r = new Tree(e - 1); r.insert(a); } else { if (!l) l = new Tree(e - 1); l.insert(a); } sum = (l ? l.sum : 0) + (r ? r.sum : 0); } } } void main() { try { for (; ; ) { const N = readInt(); auto A = new long[N]; foreach (i; 0 .. N) { A[i] = readLong(); } auto ASum = new long[N + 1]; foreach (i; 0 .. N) { ASum[i + 1] = ASum[i] ^ A[i]; } debug { auto dpBrute = new long[N + 1]; foreach_reverse (i; 0 .. N) { bool[long] app; foreach (j; i + 1 .. N + 1) { app[ASum[i] ^ ASum[j] ^ dpBrute[j]] = true; } for (long x = 0; ; ++x) { if (x !in app) { dpBrute[i] = x; break; } } } writeln("ASum = ", ASum); writeln("dpBrute = ", dpBrute); } auto dp = new long[N + 1]; auto t = new Tree(E); t.insert(ASum[N] ^ dp[N]); foreach_reverse (i; 0 .. N) { Tree u = t; foreach_reverse (e; 0 .. E) { if (ASum[i] & 1L << e) { if ((u.r ? u.r.sum : 0) == 1L << e) { dp[i] |= 1L << e; u = u.l; } else { u = u.r; } } else { if ((u.l ? u.l.sum : 0) == 1L << e) { dp[i] |= 1L << e; u = u.r; } else { u = u.l; } } if (!u) { break; } } t.insert(ASum[i] ^ dp[i]); } debug { writeln("dp = ", dp); } writeln(dp[0] ? "Takahashi" : "Takanashi"); } } catch (EOFException e) { } }