시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 512 MB 0 0 0 0.000%

## 문제

Kotori is interested in skiing. The skiing field is an infinite strip going along $y$-axis on the 2-dimensional plane where all points $(x, y)$ in the field satisfies $-m \le x \le m$. When skiing, Kotori cannot move out of the field, which means that the absolute value of his $x$-coordinate should always be no more than $m$. There are also $n$ segments on the ground which are the obstacles and Kotori cannot move across the obstacles either.

Kotori will start skiing from $(0, -10^{10^{10^{10^{10}}}})$ (you can regard this $y$-coordinate as a negative infinity) and moves towards the positive direction of the $y$-axis. Her vertical (parallel to the $y$-axis) speed is always $v_y$ which cannot be changed, however she can control her horizontal (parallel to the $x$-axis) speed in the interval of $[-v_x, v_x]$. The time that Kotori changes her velocity can be neglected.

Your task is to help Kotori calculate the minimum value of $v_x^*$ that once $v_x>v_x^*$ she can safely ski through the skiing field without running into the obstacles.

## 입력

There is only one test case in each test file.

The first line of the input contains three positive integers $n$, $m$ and $v_y$ ($1 \le n \le 100$, $1 \le m \le 10^4$, $1 \le v_y \le 10$), indicating the number of obstacles, the half width of the skiing field and the vertical speed.

For the following $n$ lines, the $i$-th line contains four integers $x_1$, $y_1$, $x_2$ and $y_2$ ($-m \le x_1, x_2 \le m$, $-10^4 \le y_1, y_2 \le 10^4$, $x_1 \ne x_2$ or $y_1 \ne y_2$) indicating the $i$-th obstacle which is a segment connecting point $(x_1, y_1)$ and $(x_2, y_2)$, both inclusive (that is to say, these two points are also parts of the obstacle and cannot be touched). It's guaranteed that no two obstacles intersect with each other.

## 출력

Output one line containing one number indicating the minimum value of $v_x^*$. If it is impossible for Kotori to pass through the skiing field, output "-1" (without quotes) instead.

Your answer will be considered correct if and only if its absolute or relative error does not exceed $10^{-6}$.

## 예제 입력 1

3 2 1
-2 0 1 0
-1 4 2 4
0 1 0 3


## 예제 출력 1

1.000000000000000


## 예제 입력 2

2 1 2
-1 0 1 0
1 1 0 1


## 예제 출력 2

-1


## 예제 입력 3

2 3 7
-3 0 2 2
3 1 -2 17


## 예제 출력 3

1.866666666666666


## 예제 입력 4

1 100 1
-100 0 99 0


## 예제 출력 4

0.000000000000000