Nick is inside a rectangular black room. He knows how far away he is from each of the room's four walls. What are the possible dimensions of the room?
~1 \le T \le 10^4~
~1 \le d_1, d_2, d_3, d_4 \le 10~
The first line contains a single positive integer, ~T~, the number of test cases. ~T~ test cases follow.
Each test case consists of a single line that contains four space-separated positive integers, ~d_1~ through ~d_4~. These four integers represent how far Nick is from each of the four walls of the room.
Output the answers for the ~T~ test cases in order. There should be no blank lines in your output.
The answer for a test case should take ~K+1~ lines, where ~K~ is the number of distinct room dimensions that are attainable. The first line should contain an integer ~K~; then, the next ~K~ lines should contain two space-separated integers ~a_i~ and ~b_i~, indicating that a rectangular room of dimensions ~a_i \times b_i~ is attainable. These lines should be printed in increasing order of ~a_i~, tiebreaking in increasing order of ~b_i~.
2 1 1 1 1 1 2 3 4
1 2 2 5 3 7 4 6 5 5 6 4 7 3