Distinct Numbers

AtCoder

IDarc137_c

Time2000ms

Memory256MB

Difficulty—

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 turn, with Alice going first. In each turn, the player does the operation below. * 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. The first player to be unable to do the operation loses. Determine the winner when both players play optimally. ## Constraints * $2 \leq N \leq 3 \times 10^5$ * $0 \leq A_1 < A_2 < \cdots < A_N \leq 10^9$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $\cdots$ $A_N$ [samples]

Samples

Input #1

2
2 4

Output #1

Alice

In 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.

Input #2

3
0 1 2

Output #2

Bob

API Response (JSON)

{
  "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
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    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc137_c"
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  "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 tur...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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