9746: ABC197 —— C - ORXOR
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Description
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 $p_1, p_2, p_3, \dots p_k$.
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 $p_1, p_2, p_3, \dots p_k$.
Input
Input is given from Standard Input in the following format:
```
$N$
$A_1$ $A_2$ $A_3$ $\dots$ $A_N$
```
```
$N$
$A_1$ $A_2$ $A_3$ $\dots$ $A_N$
```
Output
Print the answer.
Constraints
- $1 \le N \le 20$
- $0 \le A_i \lt 2^{30}$
- All values in input are integers.
- $0 \le A_i \lt 2^{30}$
- All values in input are integers.
Sample 1 Input
3
1 5 7
Sample 1 Output
2
If we divide [1,5,7] into [1,5] and [7], their bitwise ORORs are 5 and 7, whose XORXOR is 2.
It is impossible to get a smaller result, so we print 2.
It is impossible to get a smaller result, so we print 2.
Sample 2 Input
3
10 10 10
Sample 2 Output
0
We should divide this sequence into [10] and [10,10].
Sample 3 Input
4
1 3 3 1
Sample 3 Output
0
We should divide this sequence into [1,3] and [3,1].