{"raw_statement":[{"iden":"problem statement","content":"You are given a non-negative integer sequence of length $N$: $A=(A_1,A_2,\\cdots,A_N)$. Here, all elements of $A$ are pairwise distinct.\nAlice and Bob will play a game. They will alternately play a turn, with Alice going first. In each turn, the player does the operation below.\n\n*   Choose the largest element in $A$ at the moment, and replace it with a smaller non-negative integer. Here, all elements in $A$ must still be pairwise distinct after this operation.\n\nThe first player to be unable to do the operation loses. Determine the winner when both players play optimally."},{"iden":"constraints","content":"*   $2 \\leq N \\leq 3 \\times 10^5$\n*   $0 \\leq A_1 < A_2 < \\cdots < A_N \\leq 10^9$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$\n$A_1$ $A_2$ $\\cdots$ $A_N$"},{"iden":"sample input 1","content":"2\n2 4"},{"iden":"sample output 1","content":"Alice\n\nIn Alice's first turn, she may replace $4$ with $0$, $1$, or $3$. If she replaces $4$ with $0$ or $1$, Bob's move in the next turn will make Alice unable to do the operation and lose. On the other hand, if she replaces $4$ with $3$, she can win regardless of Bob's subsequent moves. Thus, Alice wins in this input."},{"iden":"sample input 2","content":"3\n0 1 2"},{"iden":"sample output 2","content":"Bob"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}