Largest Mirror Section

Background

Congcong enjoys playing with arrays. One day, he discovered an interesting array pattern, which he called a "mirror section."

Problem Description

We'll say that a "mirror" section in an array is a group of contiguous elements such that somewhere in the array, the same group appears in reverse order. For example, the largest mirror section in $\{1, 2, 3, 8, 9, 3, 2, 1\}$ is length 3 (the $\{1, 2, 3\}$ part). Return the size of the largest mirror section found in the given array.

Input Format

Input is given from standard input in the following format.

A single line containing several integers, separated by spaces.

Output Format

Output is printed to standard output in the following format.

The size of the largest mirror section.

Sample

1 2 3 8 9 3 2 1

3

1 2 1 4

3

7 1 2 9 7 2 1

2

Sample Explanation

For the first sample, the array is $\{1, 2, 3, 8, 9, 3, 2, 1\}$. The section $\{1, 2, 3\}$ at the beginning has its reverse $\{3, 2, 1\}$ appearing later in the array. The length of this mirror section is 3. This is the largest such section.

For the second sample, the array is $\{1, 2, 1, 4\}$. The section $\{1, 2, 1\}$ at the beginning has its reverse $\{1, 2, 1\}$ appearing later in the array (it is itself reversed). The length is 3.

For the third sample, the array is $\{7, 1, 2, 9, 7, 2, 1\}$. The section $\{1, 2\}$ at index 1 has its reverse $\{2, 1\}$ appearing at index 5. The length is 2. The section $\{7\}$ at index 0 has its reverse $\{7\}$ appearing at index 4. The largest length is 2.

Constraints

Time limit: 1 second, Memory limit: 1024 KiB for each test case.