#codingexercise
Count number of squares in a rectangle. For example, in a matrix of n x m is given, how many squares are in it ?
We have to try out a few cases first.
If m = n = 1, we have 1
If m = n = 2, we have 4 + 1 with four unit squares and 1 two by two.
If m = n = 3, we have 9 + 4 + 1 for increasing square sizes
This follows a pattern of n^2 + n-1 ^2 + ... +1 which equals  n(n+1)(2n+1)/6

Now let us consider the case when m and n are not equal. Then we can consider the additions one extra column at a time.
Let us say m <=n,
Then we can calculate for m x m as above
For an additional column, the number of square increases by m + m-1 + m - 2 + ... + 1
With m unit squares + m-1 squares of size 2×2 and so on
This equals m(m+1)/2
But there are n-m such columns and so we have (n-m)×m(m+1)/2 squares

The total is therefore
Int getSquaresCount(int n, int m)
{
If ( n < m)
     Swap(n,m)
Return m(m+1)(2m+1)/6 + (n-m)×m(m+1)/2;
}
Question: is it possible to add more squares contained exclusively within n-m columns and m rows
We can do this for n-m × n-m square and proceed so on.