Longest Congruent Subarray

Problem Description

You are given an array $\{A\}$ of length $N$ whose elements are pairwise distinct.

Find the longest contiguous subarray whose elements are congruent modulo some $M \ge 2$. Formally, find the longest $A[L \dots R]$ and an $M \ge 2$ such that

$$A_L \equiv A_{L+1} \equiv A_{L+2} \equiv \cdots \equiv A_R \pmod M$$

(where $a \equiv b \pmod M$ means $a \bmod M = b \bmod M$).

Output only the length of this longest contiguous congruent subarray.

Input Format

The first line contains an integer $N$.

The next line contains $N$ integers $A_1, A_2, \dots, A_N$.

Output Format

Output one number: the length of the longest contiguous congruent subarray.

Sample Input

4
8 2 10 5

Sample Output

3

Note that $8, 2, 10$ are all even, so they are congruent modulo $M = 2$.

Constraints

• $1 \leq N \leq 2 \times 10^3$
• $1 \leq a_i \leq 10^{18}$