A7770 | Letter A

Little Petya learns how to write. The teacher gave pupils the task to write the letter $A$ on the sheet of paper. It is required to check whether Petya really had written the letter $A$ .

You are given three segments on the plane. They form the letter $A$ if the following conditions hold:

- Two segments have common endpoint (lets call these segments first and second), while the third segment connects two points on the different segments.
- The angle between the first and the second segments is greater than $0$ and do not exceed $90$ degrees.
- The third segment divides each of the first two segments in proportion not less than $1/4$ (i.e. the ratio of the length of the shortest part to the length of the longest part is not less than $1/4$ ).

The first line contains one integer $t$ ( $1<=t<=10000$ ) — the number of test cases to solve. Each case consists of three lines. Each of these three lines contains four space-separated integers — coordinates of the endpoints of one of the segments. All coordinates do not exceed $10^{8}$ by absolute value. All segments have positive length.

Output one line for each test case. Print «YES» (without quotes), if the segments form the letter $A$ and «NO» otherwise.