ORXOR

AtCoder

IDabc197_c

Time2000ms

Memory256MB

Difficulty—

Given is a number sequence $A$ of length $N$. Let us divide this sequence into one or more non-empty contiguous intervals. Then, for each of these intervals, let us compute the bitwise $\mathrm{OR}$ of the numbers in it. Find the minimum possible value of the bitwise $\mathrm{XOR}$ of the values obtained in this way. What is bitwise $\mathrm{OR}$?The bitwise $\mathrm{OR}$ of integers $A$ and $B$, $A\ \mathrm{OR}\ B$, is defined as follows: * When $A\ \mathrm{OR}\ B$ is written in base two, the digit in the $2^k$'s place ($k \geq 0$) is $1$ if at least one of $A$ and $B$ is $1$, and $0$ otherwise. For example, we have $3\ \mathrm{OR}\ 5 = 7$ (in base two: $011\ \mathrm{OR}\ 101 = 111$). Generally, the bitwise $\mathrm{OR}$ of $k$ integers $p_1, p_2, p_3, \dots, p_k$ is defined as $(\dots ((p_1\ \mathrm{OR}\ p_2)\ \mathrm{OR}\ p_3)\ \mathrm{OR}\ \dots\ \mathrm{OR}\ p_k)$. We can prove that this value does not depend on the order of $p_1, p_2, p_3, \dots p_k$. What is bitwise $\mathrm{XOR}$?The bitwise $\mathrm{XOR}$ of integers $A$ and $B$, $A\ \mathrm{XOR}\ B$, is defined as follows: * When $A\ \mathrm{XOR}\ B$ 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 $3\ \mathrm{XOR}\ 5 = 6$ (in base two: $011\ \mathrm{XOR}\ 101 = 110$). Generally, the bitwise $\mathrm{XOR}$ of $k$ integers $p_1, p_2, p_3, \dots, p_k$ is defined as $(\dots ((p_1\ \mathrm{XOR}\ p_2)\ \mathrm{XOR}\ p_3)\ \mathrm{XOR}\ \dots\ \mathrm{XOR}\ p_k)$. We can prove that this value does not depend on the order of $p_1, p_2, p_3, \dots p_k$. ## Constraints * $1 \le N \le 20$ * $0 \le A_i \lt 2^{30}$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $A_3$ $\dots$ $A_N$ [samples]

Samples

Input #1

3
1 5 7

Output #1

2

If we divide $[1, 5, 7]$ into $[1, 5]$ and $[7]$, their bitwise $\mathrm{OR}$s are $5$ and $7$, whose $\mathrm{XOR}$ is $2$.  
It is impossible to get a smaller result, so we print $2$.

Input #2

3
10 10 10

Output #2

0

We should divide this sequence into $[10]$ and $[10, 10]$.

Input #3

4
1 3 3 1

Output #3

0

We should divide this sequence into $[1, 3]$ and $[3, 1]$.

API Response (JSON)

{
  "problem": {
    "name": "ORXOR",
    "description": {
      "content": "Given is a number sequence $A$ of length $N$.   Let us divide this sequence into one or more non-empty contiguous intervals.   Then, for each of these intervals, let us compute the bitwise $\\mathrm{OR",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc197_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given is a number sequence $A$ of length $N$.  \nLet us divide this sequence into one or more non-empty contiguous intervals.  \nThen, for each of these intervals, let us compute the bitwise $\\mathrm{OR...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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