Buoy Beacon Signal Lattice

An oceanographic institute deploys square arrays of drifting research buoys, L buoys to a side. Every array is assembled by choosing, for each of the L rows, one L-letter lowercase beacon code from the institute's registry — the same code may be reused in more than one row. An arrangement is considered stable only if, for every index k from 0 to L-1, reading the letters of row k from left to right produces exactly the same string as reading the letters of column k from top to bottom. Given the registry, find every stable arrangement that can be built this way.

Input format

• Line 1: an integer m — the number of codes in the registry (1 <= m <= 1000).
• Line 2: m space-separated lowercase strings, the registry's codes, each of the same length L (1 <= L <= 5). No two codes in the registry are identical.

Output format

Print an integer k on the first line — the number of stable arrangements. Then, ordered lexicographically (compare arrangement 1 by its row 0, then row 1, and so on down to row L-1, against arrangement 2's rows in the same way), print each arrangement as its L rows, one code per line, with no separator line between one arrangement and the next. If k is 0, print only the line 0 and nothing else.

Constraints

• 1 <= m <= 1000
• 1 <= L <= 5 (L is the fixed length of every code)
• All codes consist of lowercase English letters a-z only.
• The registry contains no duplicate codes.
• Rows of an arrangement may reuse the same registry code more than once.

5
area lead wall lady ball

2
ball
area
lead
lady
wall
area
lead
lady

2
ab ba

2
ab
ba
ba
ab