Algorithms and Data Structures

Maximum Length of Common Subarray

Given two integer arrays a and b, you are asked to find the maximum length of the subarray that appears in both a and b.

Input

The first line of the input contains a single integer n (1 ≤ n ≤ 1000).

The second line contains n space-separated integers (0 ≤ ≤ 100).

The third line contains n space-separated integers (0 ≤ ≤ 100).

Output

The program should print the maximum length of the common subarray.

Examples

Input

Output

4 1 2 4 2 0 4 2 1

2

3 5 5 5 5 5 5

3

Explanation

  1. The longest common subarray is 4 2 that’s common in both of the given arrays ⇒ 2 length

  2. The two arrays are equal ⇒ the longest common subarray is the given array itself ⇒ 3 length

Constraints

Time limit: 2 seconds

Memory limit: 512 MB

Output limit: 1 MB

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