F. El mask mesh hena
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Given an array $$$a$$$ of length $$$n$$$.

There is a set $$$S$$$ where it contains the bitwise-OR of all subarrays of the array $$$a$$$.

Your task is to print the bitwise-AND of all numbers in the set $$$S$$$.

Input

The first line contains an integer $$$n (1 \le n \le 200000)$$$ — the length of the array.

The second line contains $$$n$$$ integers $$$a_1, a_2, ...., a_n$$$ $$$(1 \le a_i \le 10^9)$$$

Output

Print a single integer, the bitwise-AND of the bitwise-OR of all subarrays.

Example
Input
2
1 4
Output
0
Note

array $$$a = [1, 4], S = [1, 4, 5]$$$, bitwise-AND of $$$S$$$ = 0.

There are 3 subarrays of $$$a$$$ which are $$$[1], [4], [1, 4]$$$; the bitwise-OR of each one respectively is $$$1, 4, 5$$$.