Spices

AtCoder

IDabc236_f

Time2000ms

Memory256MB

Difficulty—

The shop supaisu-ya sells $2^N-1$ kinds of spices: Spice $1$, Spice $2$, $\ldots$, Spice $2^N-1$. One pack of each spice is in stock. For each $i = 1, 2, \ldots, 2^N-1$, Spice $i$ costs $c_i$ yen. Takahashi can buy any of these spices. He plans to make curry after getting home by choosing one or more of the bought spices and mixing them. If $k$ spices, Spice $A_1$, Spice $A_2$, $\ldots$, Spice $A_k$, are mixed, the hotness of the resulting curry is $A_1 \oplus A_2 \oplus \cdots \oplus A_k$, where $\oplus$ denotes the bitwise XOR. Takahashi wants to decide the hotness of the curry based on his feeling after getting home. For now, he will buy a set of spices that allows him to make curry of any hotness from $1$ through $2^N-1$. Print the minimum possible amount of money Takahashi pays. ## Constraints * $2 \leq N \leq 16$ * $1 \leq c_i \leq 10^9$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $c_1$ $c_2$ $\ldots$ $c_{2^N-1}$ [samples]

Samples

Input #1

2
4 5 3

Output #1

7

If Takahashi buys Spice $1$ and $3$, he can make curry of any hotness from $1$ through $3$, as follows.

*   To make curry of hotness $1$, use just Spice $1$.
*   To make curry of hotness $2$, mix Spice $1$ and Spice $3$.
*   To make curry of hotness $3$, use just Spice $3$.

Here, Takahashi pays $c_1 + c_3 = 4 + 3 = 7$ yen, which is the minimum possible amount he pays.

Input #2

4
9 7 9 7 10 4 3 9 4 8 10 5 6 3 8

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Spices",
    "description": {
      "content": "The shop supaisu-ya sells $2^N-1$ kinds of spices: Spice $1$, Spice $2$, $\\ldots$, Spice $2^N-1$. One pack of each spice is in stock. For each $i = 1, 2, \\ldots, 2^N-1$, Spice $i$ costs $c_i$ yen. Tak",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc236_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "The shop supaisu-ya sells $2^N-1$ kinds of spices: Spice $1$, Spice $2$, $\\ldots$, Spice $2^N-1$. One pack of each spice is in stock. For each $i = 1, 2, \\ldots, 2^N-1$, Spice $i$ costs $c_i$ yen. Tak...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments