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?

Constraints

~1 \le T \le 10^4~

~1 \le d_1, d_2, d_3, d_4 \le 10~

Input Specification

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 Specification

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~.

Sample Input

2
1 1 1 1
1 2 3 4

Sample Output

1
2 2
5
3 7
4 6
5 5
6 4
7 3