Problem 2: Indraneel's Experiment,
*(K Narayan Kumar, CMI)*

Indraneel's student has given him data from two sets of
experments that the student has performed. Indraneel wants to
establish a correlation between the two sets of data. Each data set
is a sequence of *N* numbers. The two data sets do not match
number for number, but Indraneel believes that this is because data
has been shifted due to inexact tuning of the equipment.

For example, consider the following two sequences:

3 8 4 23 9 11 28 2 3 22 26 8 16 12

Indraneel observes that if we consider the subsequences
`3,4,23,9` and `2,3,22,8` and examine their
successive differences we get `1,19,-14`. He considers these
to subsequences to be "identical". He would like to find the
longest such pair of subsequences so that the successive
differences are identical. Your task is to help him do this.

Input format

The first line of the input will contain a single integer
*N* indicating the number of datapoints in each of
Indraneel's student's data sets. This is followed by two lines,
each containing *N* integers.

Output format

The output consists of three lines. The first line of output contains a single integer indicating the length of the longest pair of subsequences (one from each sequence) that has identical successive differences. This is followed by two lines each containing the corresponding subsequences. If there is more than one answer, it suffices to print one.

Test Data:

You may assume that 1 ≤ *N* ≤ 300.

Example:

Here is the sample input and output corresponding to the example discussed above.

Sample Input

7 3 8 4 23 9 11 28 2 3 22 26 8 16 12

Sample Output

4 3 4 23 9 2 3 22 8

CPU Timelimit: | 3 seconds |

Memory limit: | 64M |

Grading style: | ioi |