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127 - ZOJ Monthly, June 2013 - E
Magnet Darts

Time Limit: 2 Seconds      Memory Limit: 65536 KB

There is a magnet board on the wall, and you can throw magnet darts towards it. When a magnet dart hit a point (x, y), because of the magnetism, it will be pulled to the nearest integer point (x', y'), and you can get a score of Ax' + By'.

To make the game more interesting, only the integer points in the given N-polygon (or on the border) could get score. And we assume all the throw must hit a point which is in a rectangle area, and the polygon is also in the rectangle. Your task is to calculate the average expectation of score per throw.

#### Input

There are multiple test cases. For each test case:

The first line contains four real numbers P0, Q0, P1, Q1 (0≤P0<P1≤500, 0≤Q0<Q1≤500), represents the lower left point and the upper right point of the rectangle area, all the throw must hit a point in it.

The second line contains three integers N (3≤N≤20), A, B (-100≤A, B≤100). The meaning of them is in the description above.

Next N lines, each line contains two intergers Xi, Yi, represents the ith vertex of the polygon by clockwise order, we promise each vertex is in the rectangle area.

There is a blank line between every two cases.

#### Output

One line for each case. The the average expectation of score per throw with three decimal places.

#### Sample Input

```0 0 4 3
3 1 1
2 3
4 2
3 0
```

```1.333
```

#### Hint

A throw hit a point which is outside the polygon may be pulled in it and get score.

Author: LI, Huang
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