E. Bored Bakry
time limit per test
4 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Bakry got bored of solving problems related to xor, so he asked you to solve this problem for him.

You are given an array $$$a$$$ of $$$n$$$ integers $$$[a_1, a_2, \ldots, a_n]$$$.

Let's call a subarray $$$a_{l}, a_{l+1}, a_{l+2}, \ldots, a_r$$$ good if $$$a_l \, \& \, a_{l+1} \, \& \, a_{l+2} \, \ldots \, \& \, a_r > a_l \oplus a_{l+1} \oplus a_{l+2} \ldots \oplus a_r$$$, where $$$\oplus$$$ denotes the bitwise XOR operation and $$$\&$$$ denotes the bitwise AND operation.

Find the length of the longest good subarray of $$$a$$$, or determine that no such subarray exists.

Input

The first line contains a single integer $$$n$$$ ($$$1 \le n \le 10^6$$$) — the length of the array.

The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le 10^6$$$) — elements of the array.

Output

Print a single integer — the length of the longest good subarray. If there are no good subarrays, print $$$0$$$.

Examples
Input
2
5 6
Output
2
Input
3
2 4 3
Output
0
Input
6
8 1 3 3 1 2
Output
4
Note

In the first case, the answer is $$$2$$$, as the whole array is good: $$$5 \& 6 = 4 > 5 \oplus 6 = 3$$$.

In the third case, the answer is $$$4$$$, and one of the longest good subarrays is $$$[a_2, a_3, a_4, a_5]$$$: $$$1\& 3 \& 3 \&1 = 1 > 1\oplus 3 \oplus 3\oplus 1 = 0$$$.