## Enlightened Landscape

 Time Limit: 1000ms Memory Limit: 64000KiB Accepted: 0 Submitted: 1
Enlightened landscape

# Enlightened landscape

Consider a landscape composed of connected line segments:

Above the landscape, N light bulbs are hang at the same height T in various horizontal positions. The purpose of these light bulbs is to light up the entire landscape. A landscape point is considered lit if it can "see" a light bulb directly, that is, if the line segment which links the point with a bulb does not contain any other landscape segments point.

Write a program that determines the mi-ni-mum number of light bulbs that must be switched on in order to illuminate the entire landscape.

## Input

Input file name: LIGHT.IN
Line 1: M
• An integer, the number of landscape height specifications, including the first and the last point of the landscape.
Lines 2..M+1: Xi Hi
• Two integers, separated by a space: the landscape height Hi at horizontal position Xi, 1 <= i <= M; for 1 <= i <= M-1 we have Xi+1 > Xi; any two consecutive specified points identify a segment of line in the landscape.
Line M+2: N T
• Two integers, separated by a space, the num-ber of light bulbs and their height coordinate (altitude). The bulbs are numbered from 1 to N)
Line M+3: B1 B2 ... BN
• N integers, separated by spaces: the hori-zon-tal coordinates of the light bulbs Bi+1 > Bi, 1 < i <= N-1;

## Output

File name: LIGHT.OUT
Line 1: K
• An integer: the minimum number of light bulbs to be switched on.
Line 2: L1 L2 ... LK
• K integers, separated by spaces: the labels of the light bulbs to be switched on spe-cified in increasing order of their horizontal coordinates.

## Limits

• 1 <= M <= 200
• 1 <= N <= 200
• 1 <= Xi <= 10000 for 1 <= i <= M
• 1 < T <= 10000
• 1 <= Hi <= 10000 for 1 <= i <= M
• T > Hi for any 1 <= i <= M
• X1 <= B1 and BN <=XM
• The task always has a solution for the test data. If there are multiple solutions, only one is required.

```6
1 1
3 3
4 1
7 1
8 3
11 1
4 5
1 5 6 10
```

## Sample Output

```2
1 4
```
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