Let m and n be odd integers greater than 1 . An m \times n rectangle is made up of unit squares where the squares in the top row are numbered left to right with the integers 1 through n, those in the second row are numbered left to right with the integers n+1 through 2 n, and so on. Square 200 is in the top row, and square 2000 is in the bottom row. Find the number of ordered pairs (m, n) of odd integers greater than 1 with the property that, in the m \times n rectangle, the line through the centers of squares 200 and 2000 intersects the interior of square 1099.