Course Selection

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Read problems statements in Mandarin Chinese and Russian.
Rin is attending a university.
She has M semesters to finish her program, and that program has N required courses. Each course must be taken in exactly one of the semesters.
Some courses have prerequisites: for each i from 1 to K, she must take course A[i] before course B[i].
The same course may be taught by different professors in different semesters, and how well she does will depend on which professor teaches her. Additionally, some courses may not be taught every semester.
We are given an array X representing this information. For each course i and each semester j, X[i][j] = 1 if course i is not taught in semester j. Otherwise, X[i][j] will be an integer between 0 and 100: the expected score Rin will get if she takes course i in semester j.
Rin may take any number of courses per semester, including none, as long as they are taught that semester and she has already taken any required prerequisite courses.
Help Rin to find the maximal average score she can get over her whole program.
Input
The first line contain 3 integers: N, M and K.
This is followed by N lines, each containing M integers. The j^{th} integer on the i^{th} line represents the value of X[i][j].
This is followed by K lines, each containing two integers: A[i] and B[i].
Output
Output one real number: the maximal average score, rounded to 2 digits after the decimal point.
Constraints
 1 ≤ M, N ≤ 100
 0 ≤ K ≤ 100
 1 ≤ X[i][j] ≤ 100
 1 ≤ A[i], B[i] ≤ N
 For each i, A[i] ≠ B[i].
 For different i and j, (A[i], B[i]) ≠ (A[j], B[j]).
 We guarantee there exists a way to take these N courses in M semesters.
Subtasks
Subtask 1: (20 Points) A course can have at most 1 pre request course.
Subtask 2: (80 Points) Refer to constraints above
Example
Input 1: 3 2 2 70 100 100 80 100 90 1 2 1 3 Output 1: 80.00 Input 2: 4 5 4 20 1 100 1 1 100 30 1 1 1 100 1 30 20 40 100 30 40 50 20 1 2 1 3 2 4 3 4 Output 2: 32.50
Explanation
Example case 1
The only way she can finish these 3 courses is: take course 1 in the first semester, then take courses 2 and 3 in the second semester. The average score is (70 + 80 + 90) / 3 = 80.00.
Example case 2
The optimal solution is: take course 1 in semester 1, course 2 in semester 2, course 3 in semester 3 and course 4 in semester 4.
Author:  cgy4ever 
Tester:  xiaodao 
Editorial  http://discuss.codechef.com/problems/RIN 
Tags  cgy4ever, dec14, graph, hard, maxflow 
Date Added:  9102014 
Time Limit:  1 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.6, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, SCALA, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, PERL6, TEXT, PYP3, CLOJ, FS 
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