Rectangle ABCD has all integer side lengths and its interior is divided into seven non-overlapping rectangular regions: two 8 by 10 regions, a 10 by 12 region, a 13 by 5 region, a 13 by 13 region, a 10 by 22 region and a 3 by 16 region. All linear measurements are given in feet. What is the sum of the length and width of rectangle ABCD?