CEOI 2000 Day 2 Problem 3---Enlightened landscape

Problem

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.

Task

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: X_i H_i
• Two integers, separated by a space: the landscape height H_i at horizontal position X_i, 1 <= i <= M; for 1 <= i <= M-1 we have X_i+1 > X_i; 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 ... B_N
• 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 ... L_K
• 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 <= X_i <= 10000 for 1 <= i <= M
• 1 < T <= 10000
• 1 <= H_i <= 10000 for 1 <= i <= M
• T > H_i for any 1 <= i <= M
• X₁ <= B₁ and B_N <=X_M
• The task always has a solution for the test data. If there are multiple solutions, only one is required.

  Sample Input

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

  Sample Output

  2
  1 4
  

  Solution