Bob has an array \(\{a_1,a_2,\dots,a_n\}\), each element is an integer between 1 and \(n\). Bob also has \(m\) functions whose domain and codomain are both \(\{1, 2, \dots, n\}\). Bob and Alice begin to play a game on the array. Alice plays first. For each turn, the player can choose a function \(f\) and make every \(a_i\ (1 \le i \le n)\) become \(f(a_i)\). For example, the array is \(\{1, 1, 2, 4, 5\}\) and \(f(1) = 1, f(2) = 3, f(3) = 4, f(4) = 1, f(5) = 2\). Then after the operation the array will become \(\{1, 1, 3, 1, 2\}\). If all the element in the array is same, then Alice wins and the game stops. So you can see that Bob's goal is to stop Alice. Suppose that both Alice and Bob play optimally. Alice wants to know if she can always win no matter what the array looks like.