Interesting number

Vasya loves the young mathematician in his spare time playing with integers. His favorite game - to take an integer and build it into a square. One day Vasya said that there are integers whose square ends with the same number, for example, so is the number 25: 25^2 = 625. Vasya wants to find all such numbers, and asks you to help him.

Input

In a single line of input file contains a number n (1 ≤ n ≤ 10000).

Output

The first line of output file, output the number of n-digit numbers that satisfy the condition of the problem. In the next n lines output are numbers in ascending order.

Examples