Given $q$ questions. Each question give you four points $A(x_A,y_A),B(x_B,y_B),C(x_C,y_C),D(x_D,y_D)$. Find the point of intersection of lines $AB$ and $CD$. It is guaranteed that there is only one intersection point.
### Input
- The first line contains an integer $q$.
- The next $q$ lines, each line contains eight integers $x_A,y_A,x_B,y_B,x_C,y_C,x_D,y_D$.
### Output
- Print $q$ lines. Each line, print the point of intersection for the corresponding question. Your answer will be considered correct if its absolute or relative error does not exceed $10^{-3}$. In other words, your answer, $x$, will be compared to the correct answer, $y$. If $|x-y| < 10^{-3}$, then your answer will be considered correct.
### Constraints
- $1 \le q \le 10^5$.
- $-10^6 \le x, y \le 10^6$.
### Example
Input:
```
1
0 0 1 1 1 0 0 1
```
Output:
```
0.5 0.5
```
