Tournament

AtCoder

IDabc263_f

Time2000ms

Memory256MB

Difficulty—

$2^N$ people, numbered $1$ to $2^N$, will participate in a rock-paper-scissors tournament. The tournament proceeds as follows: * The participants are arranged in a row in the order Person $1$, Person $2$, $\ldots$, Person $2^N$ from left to right. * Let $2M$ be the current length of the row. For each $i\ (1\leq i \leq M)$, the $(2i-1)$\-th and $(2i)$\-th persons from the left play a game against each other. Then, the $M$ losers are removed from the row. This process is repeated $N$ times. Here, if Person $i$ wins exactly $j$ games, they receive $C_{i,j}$ yen (Japanese currency). A person winning zero games receives nothing. Find the maximum possible total amount of money received by the $2^N$ people if the results of all games can be manipulated freely. ## Constraints * $1 \leq N \leq 16$ * $1 \leq C_{i,j} \leq 10^9$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $C_{1,1}$ $C_{1,2}$ $\ldots$ $C_{1,N}$ $C_{2,1}$ $C_{2,2}$ $\ldots$ $C_{2,N}$ $\vdots$ $C_{2^N,1}$ $C_{2^N,2}$ $\ldots$ $C_{2^N,N}$ [samples]

Samples

Input #1

Output #1

15

The initial row of the people is $(1,2,3,4)$.
If Person $2$ wins the game against Person $1$, and Person $4$ wins the game against Person $3$, the row becomes $(2,4)$.
Then, if Person $4$ wins the game against Person $2$, the row becomes $(4)$, and the tournament ends.
Here, Person $2$ wins exactly $1$ game, and Person $4$ wins exactly $2$ games, so they receive $0+6+0+9=15$ yen in total, which is the maximum possible sum.

Input #2

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Tournament",
    "description": {
      "content": "$2^N$ people, numbered $1$ to $2^N$, will participate in a rock-paper-scissors tournament. The tournament proceeds as follows: *   The participants are arranged in a row in the order Person $1$, Pers",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc263_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "$2^N$ people, numbered $1$ to $2^N$, will participate in a rock-paper-scissors tournament.\nThe tournament proceeds as follows:\n\n*   The participants are arranged in a row in the order Person $1$, Pers...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments