Toy Storage

Time Limit: 2 Seconds
Memory Limit: 65536 KB

Mom and dad have a problem: their child, Reza, never puts his toys away when he
is finished playing with them. They gave Reza a rectangular box to put his toys
in. Unfortunately, Reza is rebellious and obeys his parents by simply throwing
his toys into the box. All the toys get mixed up, and it is impossible for Reza
to find his favorite toys anymore.

Reza's parents came up with the following idea. They put cardboard partitions
into the box. Even if Reza keeps throwing his toys into the box, at least toys
that get thrown into different partitions stay separate. The box looks like
this from the top:

We want for each positive integer t, such that there exists a partition with
t toys, determine how many partitions have t, toys.

**Input**

The input consists of a number of cases. The first line consists of six integers
n, m, x1, y1, x2, y2. The number of cardboards to form the partitions is n (0
< n <= 1000) and the number of toys is given in m (0 < m <= 1000).
The coordinates of the upper-left corner and the lower-right corner of the box
are (x1, y1) and (x2, y2), respectively. The following n lines each consists
of two integers Ui Li, indicating that the ends of the ith cardboard is at the
coordinates (Ui, y1) and (Li, y2). You may assume that the cardboards do not
intersect with each other. The next m lines each consists of two integers Xi
Yi specifying where the ith toy has landed in the box. You may assume that no
toy will land on a cardboard.

A line consisting of a single 0 terminates the input.

**Output**

For each box, first provide a header stating "Box" on a line of its
own. After that, there will be one line of output per count (t > 0) of toys
in a partition. The value t will be followed by a colon and a space, followed
the number of partitions containing t toys. Output will be sorted in ascending
order of t for each box.

**Sample Input**

4 10 0 10 100 0

20 20

80 80

60 60

40 40

5 10

15 10

95 10

25 10

65 10

75 10

35 10

45 10

55 10

85 10

5 6 0 10 60 0

4 3

15 30

3 1

6 8

10 10

2 1

2 8

1 5

5 5

40 10

7 9

0

**Sample Output**

Box

2: 5

Box

1: 4

2: 1

Source:

**Asia 2003, Tehran (Iran), Preliminary**
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