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)); } void main() { debug { enum lim = 8; auto dp3 = new int[][][][](3 + 1, lim, lim, lim); foreach_reverse (i; 0 .. 3 + 1) { foreach (a; 0 .. lim) foreach (b; 0 .. lim) foreach (c; 0 .. lim) { int[] xs; foreach (j; i + 1 .. 3 + 1) { xs ~= dp3[j][a][b][c]; } if (0 < i) foreach (aa; 0 .. a) xs ~= dp3[i][aa][b][c]; if (1 < i) foreach (bb; 0 .. b) xs ~= dp3[i][a][bb][c]; if (2 < i) foreach (cc; 0 .. c) xs ~= dp3[i][a][b][cc]; xs = xs.sort.uniq.array; int x; for (x = 0; x < xs.length; ++x) { if (xs[x] != x) { break; } } dp3[i][a][b][c] = x; } } foreach (a; 0 .. lim) foreach (b; 0 .. lim) foreach (c; 0 .. lim) { if (dp3[0][a][b][c]) { writeln([a, b, c], ": ", dp3[0][a][b][c], "; ", [a, a ^ b, a ^ b ^ c]); } if (!dp3[0][a][b][c]) { // writeln([a, b, c], ": ", dp3[0][a][b][c], "; ", [a, a ^ b, a ^ b ^ c]); } if (a > 0 && b > 0 && c > 0) { assert((dp3[0][a][b][c] != 0) == (a == 0 || (a ^ b) == 0 || (a ^ b ^ c) == 0)); } } foreach (i; 0 .. 3 + 1) { writeln("i = ", i); foreach (a; 0 .. lim) { writeln("a = ", a); foreach (b; 0 .. lim) { foreach (c; 0 .. lim) { write(dp3[i][a][b][c]); } writeln(); } writeln(); } writeln(); } } try { for (; ; ) { const N = readInt(); auto A = new long[N]; foreach (i; 0 .. N) { A[i] = readLong(); } long sum; int cnt0, cnt1; foreach (i; 0 .. N) { sum ^= A[i]; if (sum == 0) ++cnt0; if (sum == 1) ++cnt1; } bool ans; ans = ans || (cnt0 >= 1); ans = ans || (cnt1 >= 2); writeln(ans ? "Takahashi" : "Takanashi"); } } catch (EOFException e) { } }