You will be given a square matrix of N rows and N columns (1 <= N <= 1000) containing positive and negative integers with absolute value not larger than 1000. You are required to compute the greatest sum achievable by walking a path, starting at any cell of the matrix and always moving downwards or rightwards. Additionally, you have to report the number of times that value is achievable. N will be in the first line of the input. N lines follow with N integers each. You should output a single line with two integers separated by a single blank space: first one is the greatest sum, second one is the number of times this value can be reached.
Case 1:
For the input provided as follows:
5
3 1 -2 1 1
-6 -1 4 -1 -4
1 1 1 1 1
2 2 2 2 2
1 1 1 1 1
Output of the program will be:
15 1
Case 1:
For the input provided as follows:
5
3 1 -2 1 1
-6 -1 4 -1 -4
1 1 1 1 1
2 2 2 2 2
1 1 1 1 1
Output of the program will be:
15 1
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