<image> New Fantasy Magic Square Puzzle
The grid of numbers shown in the image is a new type of magic square. In this square, circle any number. Then, cross out all the numbers in the same row and column as this circled number. Next, choose another uncrossed number and circle it, then cross out all the numbers in the same row and column as this new circled number. Continue this process until you have circled 6 numbers.

Obviously, each number is chosen completely at random, but no matter how you choose these numbers, their sum is always the same. What is this number? Moreover, and more importantly, why is the sum of the chosen numbers always a constant?