Joe Goes Farming!

Being the industrious type, Joe and his girlfriend Liz decide to start a farm. On their farm they have dogs, cats and hogs.

Joe notices that dogs and cats make a fight (i.e., DOGS + CATS = FIGHT). He also knows that a dog is bigger than a cat (i.e., DOG > CAT).

Being an animal lover on a budget, Liz wants to buy the least number of dogs and cats to make a shit-show. Let M be the least number of total animals (dogs and cats) she needs to do this. I.e., if m and p are positive integers satisfying m(DOG) + p(CAT) = SHITSHO, then M is the minimum possible value of m+p.

Being a meat-lover, Joe breeds hogs. His prize-winning female hog (which he affectionately names Piglet) weighs HOG pounds. Joe is so proud of Piglet, he decides to clone her. Each clone also weighs exactly HOG pounds as well.

Joe and Liz's relationship is grounded in compromise. So Joe insists that the combined weight of all his hogs in pounds is at least the number of animals Liz buys. Assuming the only hogs Joe has are his clones and Piglet, what is the square of the least number of clones Joe must create?

Note : Above the letters D, O, G, S, C, A, T, F, I, H each stand for different digits (in base 10). Also, for example, CAT denotes the number CAT, i.e., CAT has value 100C+10A+T. Naturally, O is zero.

P.S. Thank you Joe and Liz for being good sports about this!!