P-Broken-Line

Memory limit: 32 MB

In the rectangular coordinate system every point with integer coordinates is called p-point. Any segment with different ends being p-points, parallel to one of the axis of coordinates, is called p-segment. Only closed segments (with end points belonging to the segment) are taken into consideration. A broken line built from p-segments, in which every two consecutive ones are perpendicular, we call p-broken-line of degree .

Task

Write a program which:

• reads descriptions of a certain number of p-segments and coordinates of two different p-points and , from the standard input,
• determines minimum degree of a p-broken-line connecting these two points and not crossing any from given p-segments or states, that such a p-broken-line does not exist.
• writes the result to the standard output.

Input

Description of a p-point consists of two non-negative integers, being being coordinates and adequately of this p-point, separated by a single space, These numbers are from range . The first line of the standard input contains only the description of the p-point . The second line contains only the description of the p-point . The third line consists exactly of one non-negative integer n being the number of p-segments, . Each of next lines consists of descriptions of exactly two p-points, separated by a single space. These are coordinates of the ends of one p-segment.

Output

The first and the the only line of standrd output should contain either one number being minimum degree of p-broken-line connecting points and and not crossing any of given p-segments, or the word "BRAK", if a p-broken-line having above-mentioned properties does not exist.

Example

For the input data:

1 2
3 4
5
0 0 7 0
0 5 7 5
2 2 2 7
4 0 4 3
3 2 6 2

the correct result is:

5

Task author: Grzegorz Jakacki.