ABC Tournament

AtCoder

IDabc188_c

Time2000ms

Memory256MB

Difficulty—

$2^N$ players, labeled $1$ through $2^N$, will compete against each other in a single-elimination programming tournament. The rating of Player $i$ is $A_i$. Any two players have different ratings, and a match between two players always results in the victory of the player with the higher rating. The tournament looks like a perfect binary tree. Formally, the tournament will proceed as follows: * For each integer $i = 1, 2, 3, \dots, N$ in this order, the following happens. * For each integer $j (1 \le j \le 2^{N - i})$, among the players who have never lost, the player with the $(2j - 1)$\-th smallest label and the player with the $2j$\-th smallest label play a match against each other. Find the label of the player who will take **second place**, that is, lose in the final match. ## Constraints * $1 \le N \le 16$ * $1 \le A_i \le 10^9$ * $A_i$ are pairwise different. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $A_3$ $\dots$ $A_{2^N}$ [samples]

Samples

Input #1

2
1 4 2 5

Output #1

2

First, there will be two matches between Players $1$ and $2$ and between Players $3$ and $4$. According to the ratings, Players $2$ and $4$ will win.  
Then, there will be a match between Players $2$ and $4$, and the tournament will end with Player $4$ becoming champion.  
The player who will lose in the final match is Player $2$, so we should print $2$.

Input #2

2
3 1 5 4

Output #2

1

First, there will be two matches between Players $1$ and $2$ and between Players $3$ and $4$. According to the ratings, Players $1$ and $3$ will win.  
Then, there will be a match between Players $1$ and $3$, and the tournament will end with Player $3$ becoming champion.  
The player who will lose in the final match is Player $1$, so we should print $1$.

Input #3

4
6 13 12 5 3 7 10 11 16 9 8 15 2 1 14 4

Output #3

API Response (JSON)

{
  "problem": {
    "name": "ABC Tournament",
    "description": {
      "content": "$2^N$ players, labeled $1$ through $2^N$, will compete against each other in a single-elimination programming tournament.   The rating of Player $i$ is $A_i$. Any two players have different ratings, a",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc188_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "$2^N$ players, labeled $1$ through $2^N$, will compete against each other in a single-elimination programming tournament.  \nThe rating of Player $i$ is $A_i$. Any two players have different ratings, a...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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