XOR to All

AtCoder

IDarc135_c

Time2000ms

Memory256MB

Difficulty—

You are given a sequence of non-negative integers $A = (A_1, \ldots, A_N)$. You can do the operation below any number of times (possibly zero). * Choose an integer $x\in {A_1,\ldots,A_N}$. * Replace $A_i$ with $A_i\oplus x$ for every $i$ ($\oplus$ denotes the bitwise $\mathrm{XOR}$ operation). Find the maximum possible value of $\sum_{i=1}^N A_i$ after your operations. What is bitwise $\mathrm{XOR}$?The bitwise $\mathrm{XOR}$ of non-negative integers $A$ and $B$, $A \oplus B$, is defined as follows: * When $A \oplus B$ is written in base two, the digit in the $2^k$'s place ($k \geq 0$) is $1$ if exactly one of $A$ and $B$ is $1$, and $0$ otherwise. For example, we have $3 \oplus 5 = 6$ (in base two: $011 \oplus 101 = 110$). ## Constraints * $1\leq N \leq 3\times 10^{5}$ * $0\leq A_i < 2^{30}$ ## Input Input is given from Standard Input from the following format: $N$ $A_1$ $\ldots$ $A_N$ [samples]

Samples

Input #1

5
1 2 3 4 5

Output #1

19

Here is a sequence of operations that achieves $\sum_{i=1}^N A_i = 19$.

*   Initially, the sequence $A$ is $(1,2,3,4,5)$.
*   An operation with $x = 1$ changes it to $(0,3,2,5,4)$.
*   An operation with $x = 5$ changes it to $(5,6,7,0,1)$, where $\sum_{i=1}^N A_i = 5 + 6 + 7 + 0 + 1 = 19$.

Input #2

5
10 10 10 10 10

Output #2

50

Doing zero operations achieves $\sum_{i=1}^N A_i = 50$.

Input #3

5
3 1 4 1 5

Output #3

API Response (JSON)

{
  "problem": {
    "name": "XOR to All",
    "description": {
      "content": "You are given a sequence of non-negative integers $A = (A_1, \\ldots, A_N)$. You can do the operation below any number of times (possibly zero). *   Choose an integer $x\\in {A_1,\\ldots,A_N}$. *   Repl",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc135_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a sequence of non-negative integers $A = (A_1, \\ldots, A_N)$. You can do the operation below any number of times (possibly zero).\n\n*   Choose an integer $x\\in {A_1,\\ldots,A_N}$.\n*   Repl...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments