Kode Festival

AtCoder

IDrelay_c

Time2000ms

Memory256MB

Difficulty—

_Kode Festival_ is an anual contest where the hardest stone in the world is determined. (Kode is a Japanese word for "hardness".) This year, $2^N$ stones participated. The hardness of the $i$\-th stone is $A_i$. In the contest, stones are thrown at each other in a knockout tournament. When two stones with hardness $X$ and $Y$ are thrown at each other, the following will happen: * When $X$ > $Y$: The stone with hardness $Y$ will be destroyed and eliminated. The hardness of the stone with hardness $X$ will become $X-Y$. * When $X$ = $Y$: One of the stones will be destroyed and eliminated. The hardness of the other stone will remain the same. * When $X$ < $Y$: The stone with hardness $X$ will be destroyed and eliminated. The hardness of the stone with hardness $Y$ will become $Y-X$. The $2^N$ stones will fight in a knockout tournament as follows: 1. The following pairs will fight: (the $1$\-st stone versus the $2$\-nd stone), (the $3$\-rd stone versus the $4$\-th stone), ... 2. The following pairs will fight: (the winner of ($1$\-st versus $2$\-nd) versus the winner of ($3$\-rd versus $4$\-th)), (the winner of ($5$\-th versus $6$\-th) versus the winner of ($7$\-th versus $8$\-th)), ... 3. And so forth, until there is only one stone remaining. Determine the eventual hardness of the last stone remaining. ## Constraints * $1 \leq N \leq 18$ * $1 \leq A_i \leq 10^9$ * $A_i$ is an integer. ## Input The input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ : $A_{2^N}$ [samples]

Samples

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API Response (JSON)

{
  "problem": {
    "name": "Kode Festival",
    "description": {
      "content": "_Kode Festival_ is an anual contest where the hardest stone in the world is determined. (Kode is a Japanese word for \"hardness\".) This year, $2^N$ stones participated. The hardness of the $i$\\-th ston",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "relay_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "_Kode Festival_ is an anual contest where the hardest stone in the world is determined. (Kode is a Japanese word for \"hardness\".)\nThis year, $2^N$ stones participated. The hardness of the $i$\\-th ston...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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