CSES - Line Segment Intersection
• Time limit: 1.00 s
• Memory limit: 512 MB
There are two line segments: the first goes through the points $(x_1,y_1)$ and $(x_2,y_2)$, and the second goes through the points $(x_3,y_3)$ and $(x_4,y_4)$.

Your task is to determine if the line segments intersect, i.e., they have at least one common point.

Input

The first input line has an integer $t$: the number of tests.

After this, there are $t$ lines that describe the tests. Each line has eight integers $x_1$, $y_1$, $x_2$, $y_2$, $x_3$, $y_3$, $x_4$ and $y_4$.

Output

For each test, print "YES" if the line segments intersect and "NO" otherwise.

Constraints
• $1 \le t \le 10^5$
• $-10^9 \le x_1, y_1, x_2, y_2, x_3, y_3, x_4, y_4 \le 10^9$
• $(x_1,y_1) \neq (x_2,y_2)$
• $(x_3,y_3) \neq (x_4,y_4)$
Example

Input:
5 1 1 5 3 1 2 4 3 1 1 5 3 1 1 4 3 1 1 5 3 2 3 4 1 1 1 5 3 2 4 4 1 1 1 5 3 3 2 7 4

Output:
NO YES YES YES YES