{"problem":{"name":"Distinct Numbers","description":{"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. Alice and Bob will play a game. They will alternately play a tur","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc137_c"},"statements":[{"statement_type":"Markdown","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.\n\n## Constraints\n\n*   $2 \\leq N \\leq 3 \\times 10^5$\n*   $0 \\leq A_1 < A_2 < \\cdots < A_N \\leq 10^9$\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$A_1$ $A_2$ $\\cdots$ $A_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc137_c","tags":[],"sample_group":[["2\n2 4","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."],["3\n0 1 2","Bob"]],"created_at":"2026-03-03 11:01:13"}}