Bored Bakry
Description
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.
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.
Print a single integer — the length of the longest good subarray. If there are no good subarrays, print $0$.
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 $0$.
Samples
2
5 6
2
3
2 4 3
0
6
8 1 3 3 1 2
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 $[a_2, a_3, a_4, a_5]$: $1\& 3 \& 3 \&1 = 1 > 1\oplus 3 \oplus 3\oplus 1 = 0$.