A14618. Bored Bakry

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](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) and $\&$ denotes the [bitwise AND operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND).

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 $0$ .

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 $[a_2, a_3, a_4, a_5]$ : $1\& 3 \& 3 \&1 = 1 > 1\oplus 3 \oplus 3\oplus 1 = 0$ .