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# Increasing Path in Matrix

Problem Description

Given a 2D integer matrix A of size `N x M`.

From A[i][j] you can move to A[i+1][j], if A[i+1][j] > A[i][j], or can move to A[i][j+1] if A[i][j+1] > A[i][j].

The task is to find and output the longest path length possible if we start from the cell (0, 0) and want to reach cell (N - 1, M - 1).

NOTE:

• If there doesn't exist a path return -1.

Problem Constraints

1 <= N, M <= 103

1 <= A[i][j] <= 108

Input Format

First and only argument is an 2D integer matrix A of size `N x M`.

Output Format

Return a single integer denoting the length of longest path in the matrix if no such path exists return -1.

Example Input

Input 1:

``` A = [  [1, 2]
[3, 4]
]
```

Input 2:

``` A = [  [1, 2, 3, 4]
[2, 2, 3, 4]
[3, 2, 3, 4]
[4, 5, 6, 7]
]
```

Example Output

Output 1:

``` 3
```

Output 2:

``` 7
```

Example Explanation

Explanation 1:

``` Longest path is either 1 2 4 or 1 3 4.
```

Explanation 2:

``` Longest path is 1 2 3 4 5 6 7.
```

NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a question? Checkout Sample Codes for more details.
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