Restore Cube

题意翻译

给定三维空间内8个点，位于整数点（立方体的侧面可能不平行于坐标轴），每个点的xyz坐标被打乱，问是否 能通过调整每个点的xyz坐标使得这八个点构成一个正方体（原始坐标是没有重复的） 输入 8个坐标见样例 输出 如果有解，输出调整后的8个坐标

题目描述

Peter had a cube with non-zero length of a side. He put the cube into three-dimensional space in such a way that its vertices lay at integer points (it is possible that the cube's sides are not parallel to the coordinate axes). Then he took a piece of paper and wrote down eight lines, each containing three integers — coordinates of cube's vertex (a single line contains coordinates of a single vertex, each vertex is written exactly once), put the paper on the table and left. While Peter was away, his little brother Nick decided to play with the numbers on the paper. In one operation Nick could swap some numbers inside a single line (Nick didn't swap numbers from distinct lines). Nick could have performed any number of such operations. When Peter returned and found out about Nick's mischief, he started recollecting the original coordinates. Help Peter restore the original position of the points or else state that this is impossible and the numbers were initially recorded incorrectly.

输入输出格式

输入格式

Each of the eight lines contains three space-separated integers — the numbers written on the piece of paper after Nick's mischief. All numbers do not exceed $ 10^{6} $ in their absolute value.

输出格式

If there is a way to restore the cube, then print in the first line "YES". In each of the next eight lines print three integers — the restored coordinates of the points. The numbers in the $ i $ -th output line must be a permutation of the numbers in $ i $ -th input line. The numbers should represent the vertices of a cube with non-zero length of a side. If there are multiple possible ways, print any of them. If there is no valid way, print "NO" (without the quotes) in the first line. Do not print anything else.

输入输出样例

输入样例 #1

0 0 0
0 0 1
0 0 1
0 0 1
0 1 1
0 1 1
0 1 1
1 1 1

输出样例 #1

YES
0 0 0
0 0 1
0 1 0
1 0 0
0 1 1
1 0 1
1 1 0
1 1 1

输入样例 #2

0 0 0
0 0 0
0 0 0
0 0 0
1 1 1
1 1 1
1 1 1
1 1 1

输出样例 #2

NO