Write a program which multiplies two matrices. The matrices may be any size, contain integers, and will come as input from the user. Each matrix will be input with the columns separated by spaces and the rows each on a new line. The end of each matrix will be specified by an empty line with no integers. Your program should print the resulting matrix with each column separated by a space, and each row on a new line.

Remember that the matrix product is defined as:

(AB)_ij = sum of (A_ik * B_kj) for k = 1 to m (where m is the number of columns in A)

Your program should output an error if the dimensions of the input matrices are incompatible (the number of columns in the first is not equal to the number of rows in the second).

Each input matrix should be stored in a multidimensional integer array. You may also want to use a multidimensional array to store the result matrix. All three matrices have sizes less or equal 10 by 10.

The program should print a string of text to the terminal before getting input from the user. A session should look like one of the following examples (including whitespace and formatting), with a possibly matrix in the output:

Enter first matrix: 1 2 3 4 5 6 Enter second matrix: 7 8 9 0 1 2 The product is: 28 14 79 44 

Enter first matrix: 1 2 3 Enter second matrix: 4 5 6 The two matrices have incompatible dimensions.