Book of programming problems

Complexity (1-100): 35

N matches on a plane constitute a figure (N≤15). A figure A is symmetric to figure B iff there exists an axis of symmetry such that B can be obtained by flipping A around that axis.

Obviously, each figure can be flipped by moving its matches. Matches cannot be broken, but can be put one on another.

Write a program flipping a figure by moving minimal number of matches. Input data is stored in a file containing N in the first line, then N lines each containing space-separated coordinates of matches ends (x1, y1) - (x2, y2) of figure A. The program should output 1) a number of moved matches and 2) N lines containing coordinates of matches in the symmetric figure B.

Example:

     INPUT.TXT        OUTPUT
     3                1
     1 0 1 5          9 0 9 5
     2 4 5 0          2 4 5 0
     5 0 8 4          5 0 8 4

Notes. All coordinates are integer. The program is allowed to run no longer than 1 sec.