Given a matrix a, determine whether or not a legal knight's tour is present. The knight's tour always follows the pattern 1, 2, 3, ... but it need not fill the entire matrix. Any unused squares contain zeros. Your function should return true if the counting sequence from 1 to n represents a knight's tour, and false if not.

Example

The matrix a as given below is a legal knight's tour. The middle square is unreachable, but since it contains a zero, it satisfies the condition. The function should return TRUE.

7     2     5
4     0     8
1     6     3

Here is another legal (if short) knight's tour. The test suite will always contain at least one move (i.e. the counting sequence [1 2]). Note the matrix is not required to be square.

1     0     0
0     0     2

Here is an illegal knight's tour. Everything is fine up until the jump from 14 to 15, which is illegal because it jumps from row 4 to row 1.

 15     5    12     3
  0     2     9     6
  8    11     4    13
  1    14     7    10