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