Tony and Maria each chose a positive integer and told these to Lenny, but to nobody else. Lenny said: "Either the sum of your two numbers is 70 or the product of your two numbers is 70." (Because Tony and Maria have complete high school mathematics they quickly determine that is not possible for both the sum and product to equal 70.) Tony then said: "This is not enough information for me to know what Maria's number is." Next, Maria said: "I do not have enough information to know what Tony's number is." This information is (surprisingly) enough information to know what Maria's number is. What is Maria's number? Justify your answer.