Wesley the robot has been in a car accident and needs surgery. Unfortunately, ordinary surgical tools are not much use on a robot, so his surgeon Leo must work with Wesley's internal subsystem values instead.

Wesley has ~n~ subsystems, with values ~a_1,a_2,\dots,a_n~.

To perform the operation, Leo must choose one of Wesley's subsystem values as a calibration value ~x~. That is, ~x=a_j~ for some ~1\le j\le n~.

The success score of choosing ~x~ is

$$\displaystyle S(x)=\sum_{i=1}^{n}(a_i\oplus x), $$

where ~\oplus~ denotes the bitwise XOR operation.

Leo wants to choose a calibration value that maximises the success score, ~S(x)~. If several possible values of ~x~ give the same maximum success score, he wants to choose the smallest value of ~x~ that does so.

Determine the value of ~x~ that Leo should use.

Bitwise XOR compares two integers bit by bit. A bit in the result is (1) exactly when the corresponding bits of the two integers are different.

Input

The first line contains a single integer ~n~ (~1\le n\le 10^5~), the number of Wesley's subsystems.

The second line contains ~n~ space-separated integers ~a_1,a_2,\dots,a_n~ (~0\le a_i\le 10^9~), the value of each subsystem.

Output

Output a single integer ~x~: the smallest subsystem value that maximises ~S(x)~.

Example

Input 1

3
1 2 1

Output 1

2

Clearly there are only two distinct subsystem values here that Leo could pick: ~1~ or ~2~.

• Picking ~1~ gives ~S(1)=1\oplus1+2\oplus1+1\oplus1=0+3+0=3~.
• Picking ~2~ gives ~S(2)=1\oplus2+2\oplus2+1\oplus2=3+0+3=6~.

Thus, picking ~2~ maximises the success score of Leo's surgery.

Input 2

4
3 1 2 0

Output 2

0

Input 3

5
5 5 5 5 5

Output 3

5