Rat In A Labyrinth

Problem Description

Jenny is in the process of creating a unique cardboard labyrinth composed of various room$-$like structures, all made from cardboard pieces. Her objective is to ensure that the entrances to these rooms are exclusively positioned along the outer edges of the labyrinth.

To begin, Jenny starts with a rectangular piece of cardboard with dimensions $"$m$"$ units in length and $"$n$"$ units in height. She also has several straight cardboard pieces at her disposal. Jenny's plan is to insert these cardboard pieces inside the rectangular cardboard in a manner that each inserted piece runs parallel to one of the rectangle's sides. This arrangement will form distinct room$-$like structures within the labyrinth. Jenny prefers rooms that have precisely four sides, and she designs her labyrinth with such rooms exclusively. Once the labyrinth is complete, Jenny is eager to play with it and decides to place her pet rat inside for a playful adventure. Now, she aims for finding the percentage probability of the rat successfully exiting the labyrinth rounded to the nearest integer value.

Given that the lower$-$left corner of the labyrinth is situated at coordinates $(0,0)$ within quadrant one, and with knowledge of the labyrinth's length, height, the placement of straight cardboard pieces within it$,$ print the percentage probability of the rat successfully exiting the labyrinth rounded to the nearest integer value.

Note : It is assured that the lines are valid and unique.

Constraints

$0<=$ x$1,$ x$2,$ y$1,$ y$2<=100$

$0<=$ m$,$n $<=100$

Input

First line consists of two space separated integers, m and n denoting the length and height of the cardboard box.

Second line consists of an integer T$,$ denoting the number of straight card board pieces that are inserted in the cardboard box as stated above.

Next T lines will have $4$ integers denoting the starting and ending points of the straight cardboard pieces where they are placed. First two integers denotes $($x$1,$y$1)$ and the next two denotes $($x$2,$y$2).$

Output

Print the percentage probability of the rat successfully exiting the labyrinth rounded to the nearest integer value.

Time Limit $($secs$)$

$1$

Examples

Example $1$

Input

$44$

$5$

$1013$

$0343$

$1222$

$2023$

$1121$

Output

$67$

Explanation

If we visualize the the above labyrinth, it will be like below.

com.tcs$.$cv$.$automata.ei$.$middleware.DocxToHtmlConverter@$7$c$351808$:image$1.$png

The given lines divides the cardboard into $6$ parts among which $2$ parts have no entrance. Thus escape rate of rat from the labyrinth will be number of rooms from which rat can exit$)/($total number of rooms$)*100$ i$.$e$.,(4/6)*100$ which is $(0\mathrm{.}66666..)*100=66\mathrm{.}666..,$ which on rounding off to the nearest integer will be $67.$

Example $2$

Input

$34$

$3$

$1014$

$2124$

$1131$

Output

$100$

Explanation

If we visualize the the above labyrinth, it will be like below.

com.tcs$.$cv$.$automata.ei$.$middleware.DocxToHtmlConverter@$7$c$351808$:image$2.$png

The given lines divides the cardboard into $4$ parts and all parts have entrance. Thus escape rate of rat from the labyrinth will be number of rooms from which rat can exit$)/($total number of rooms$)*100$ i$.$e$.,(4/4)*100$ which is $(1)*100=100,$ which on rounding off to the nearest integer will be $100.$