CF23D.Tetragon

You're given the centers of three equal sides of a strictly convex tetragon. Your task is to restore the initial tetragon.

给你一个严格凸四边形三条等长边的中点。你的任务是还原出原始的四边形。

The first input line contains one number T — amount of tests (1 ≤ T ≤ 5·104). Each of the following T lines contains numbers _x_1, _y_1, _x_2, _y_2, _x_3, _y_3 — coordinates of different points that are the centers of three equal sides (non-negative integer numbers, not exceeding 10).

第一行输入包含一个数字 $T$ —— 测试用例的数量（$1 \leq T \leq 5\cdot10^4$）。接下来的 $T$ 行中，每行包含六个数字 $x_1, y_1, x_2, y_2, x_3, y_3$ —— 分别为三个相等边的中心点的坐标（均为不超过 $10$ 的非负整数）。

For each test output two lines. If the required tetragon exists, output in the first line YES, in the second line — four pairs of numbers — coordinates of the polygon's vertices in clockwise or counter-clockwise order. Don't forget, please, that the tetragon should be strictly convex, i.e. no 3 of its points lie on one line. Output numbers with 9 characters after a decimal point.

If the required tetragon doen't exist, output NO in the first line, and leave the second line empty.

对每个测试用例输出两行。如果所要求的四边形存在，则第一行输出 YES，第二行输出四组数——即该四边形顶点的坐标（按顺时针或逆时针顺序排列）。请注意，该四边形必须是严格凸的，即其任意三点不共线。所有数字需保留小数点后 9 位。

如果所要求的四边形不存在，则第一行输出 NO，第二行留空。