Snake

A "snake" is defined as a sequence of adjacent consecutively increasing integers (incrementing by one) embedded in and twisting through a larger matrix. The sequence can turn north, south, east, or west, but not diagonally. A snake sequence may also be straight.

Given the matrix a, return the longest snake sequence in the variable b. a is an array containing positive integers. b is a column vector containing the linear index of this sequence, beginning with the smallest number in the snake sequence. For example, when

a = [ 14    16    13
      15    15    14
      16    10     9]

create

b = [ 7
      8
      5
      4 ]

Another example is

a = [  1     2     3
       4     7     4
       5     6     5]

b = [ 1
      4
      7
      8
      9
      6
      5 ]

Each matrix will have exactly one snake sequence longer than all others. In addition, a will never be a vector. That is, the smallest dimension of a will always be greater than one.

Note: Linear (or absolute) indexing is a way to index into a 2-D matrix with one number. Linear indexing is column-oriented, so if

a = [ 14    16    13
      15    15    14
      16    10     9]

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