$ cat lo_instance.txt 
1 1
2 2
3 3
1 3
3 1
$ python3.6 lo_solver.py 5 < lo_instance.txt 
0: 0 1
1: 0 4
2: 1 0
3: 1 1
4: 1 2
5: 1 3
6: 1 4
7: 2 1
8: 2 2
9: 2 4
10: 3 1
11: 3 3
12: 4 0
13: 4 1
14: 4 2
$ cat lo_instance_bad.txt 
0 0
0 3
1 2
2 1
2 2
2 4
3 1
4 0
$ python3.6 lo_solver.py 5 < lo_instance_bad.txt 
0: 0 2
1: 0 3
2: 0 4
3: 1 0
4: 1 1
5: 1 2
6: 2 1
7: 2 4
8: 3 1
9: 3 2
10: 3 3
11: 4 0
12: 4 2
There is no solution.
Residual has non-zero entries at
  0: 0 2
  1: 4 1
  (2 non-zero entries)
$