A. Reflecting
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

March is visiting the beautiful city of Belobog!

The city of Belobog can be modeled through a coordinate system. March is currently at the point $$$(x_1,y_1)$$$ and she would like to get to the point $$$(x_2,y_2)$$$.

Due to technological advancements, most people prefer to teleport instead of walk. March can perform the following operation any number of times:

  • Choose two integers $$$x$$$ and $$$y$$$. Then, she will teleport to the location that is the reflection of her current location across the point $$$(x,y)$$$.

Is it possible to reach $$$(x_2,y_2)$$$ through any number of operations?

Input

The first line contains an integer $$$t$$$ ($$$1 \leq t \leq 10^4$$$) – the number of test cases. Descriptions of the test case follows.

The first line of each test case contains four integers $$$x_1,y_1,x_2,y_2$$$ ($$$-10^9 \leq x_1,x_2,y_1,y_2 \leq 10^9$$$).

Output

For each test case, output YES if it is possible, and NO otherwise. The letters may be outputted in uppercase or lowercase.

Example
Input
5
2 3 2 5
-15 20 -31 24
24 31 93 77
0 0 0 0
1000000000 999999999 -999999999 -1000000000
Output
YES
YES
NO
YES
NO
Note

In the first test case, March can reflect across the point $$$(2,4)$$$ to reach $$$(2,5)$$$ immediately.

In the second test case, March can first teleport through the point $$$(-20, 22)$$$ to reach $$$(-25, 24)$$$, then across the point $$$(-28, 24)$$$ to reach $$$(-31, 24)$$$.

In the third test case, we can show that March cannot reach $$$(93,77)$$$ no matter which operations she use.