shaan is making his famous Ishaan soup for all the new TA$$s to drink for initiation. He has the following ingredients: carrots, potatoes, mangoes, lettuce, avocados, eggs, and last but not least...tears $($of CIS$1600$ students$).$ We know that the number of each of the distinct ingredients is a positive odd integer, and that the total number of ingredients added into the soup is $721.$ If we define a soup as the number of times each ingredient was put into the soup $($e$.$g$.,$ a single soup could be made with $1$ carrot, $3$ potatoes, $5$ mangoes, $7$ lettuce, $9$ avocados, $11$ eggs, and $685$ tears$),$ how many soups can be made?