Sereja and Functions (Challenge)

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Read problems statements in mandarin chinese and vietnamese as well.
Sereja is stuck with a problem and asks for your help. You readily agree to help Sereja and he poses the following problem to you.
Sereja has a matrix A of size N x N. Each cell in row i and column j contains a number A[i][j]. Every element of the matrix can either be 0 or 1. Initially, all the elements are zero.
Sereja informs you that he only likes the functions of the form
Here the division is integer division, i.e. x/y means integer division of x by y.
Sereja can choose a set of integers a_{1}, a_{2}, b_{1}, b_{2}, c_{1}, c_{2}, d and two other integers l, r and applies the function f to the matrix as follows. He will substitute 1 in the every cell (i, j) where l ≤ i ≤ r and j = f(i).
Sereja gives you a matrix A after applying a certain number of functions to it. He asks you to find the minimal amount of functions such that after applying them Sereja will get the matrix A. You need not create the matrix A exactly, you are allowed to have at most 100 distinct cells in the matrix obtained after your operations and the matrix A. Your task is to minimize the number of such functions applied.
Input
The first line of input contains an integer T denoting the number of test cases.
First line of each test case contains an integer N. Each of the next N lines contains N digits (zero or one) without spaces denoting the matrix A.
Output
For each test case in first line output an integer corresponding to the number of functions Q.
Next Q lines should contain information about functions. Each lines should contain set of integers a_{1}, a_{2}, b_{1}, b_{2}, c_{1}, c_{2}, d, l, r.
The following constraints must be satisfied for the output.
 0 ≤ Q ≤ N*N
 N ≤ a_{1}, b_{1}, c_{1}, d ≤ N
 1 ≤ a_{2}, b_{2}, c_{2} ≤ N
 1 ≤ l ≤ r ≤ N
Constraints
 1 ≤ T ≤ 20
 1 ≤ N ≤ 100
Tests generation
There will be 10 official tests. During contest you will be able to get your score on first 2 tests. After contest there will be rejudge on full tests set.
In every test, T is equal to 20 and N is chosen randomly in the range [95, 100]. Further for each test case integer K is chosen:
 For first 5 tests, K is chosen randomly in range [1, 5]
 For next 5 tests, K is chosen randomly in range [50, 100]
 For next 5 tests, K is chosen randomly in range [500, 1000]
 For next 5 tests, K is chosen randomly in range [1000, 3000]
After K is chosen we generate K functions in next way:
 With probability 1/3, a_{1} = b_{1} = 0
 With probability 2/3, a_{1} = 0
 For all other numbers, the way of generation is hidden
Scoring
You will receive a WA if the operation doesn't satisfy the output constraints specified in the statement or the number of distinct cells in the final matrix after applying all the operations exceeds 100.
Lets S denote the sum of Q / (N * N + 1  ONES) (where ONES is number of digit 1 in given matrix) for all the test cases. Your score will be to S which you should try to minimize.
Example
Input: 1 5 00010 00100 01000 10000 11111 Output: 2 0 1 0 1 1 1 5 1 4 0 1 0 1 0 1 5 1 5
Author:  sereja 
Editorial  https://discuss.codechef.com/problems/SEAFUNC 
Tags  challenge, greedy, math, sept17, sereja 
Date Added:  21112015 
Time Limit:  1 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.5, PYPY, 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, SCM chicken, CLOJ, FS 
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