B'Bessie has recently started playing a famous card game. In the game, there is only one deck of cards, consisting of a "draw 0 " cards, b "draw 1 " cards, c "draw 2 " cards, and 5 special cards. At the start of the game, all cards are in the randomly shuffled deck. Bessie starts the game by drawing the top 5 cards of the deck. She may then play "draw x " cards from the hand to draw the next x cards from the top of the deck. Note that every card can only be played once, special cards cannot be played, and if Bessie uses a "draw 2 " card when there is only 1 card remaining in the deck, then she simply draws that remaining card. Bessie wins if she draws all 5 special cards. Since Bessie is not very good at math problems, she wants you to find the probability that she wins, given that the deck is shuffled randomly over all (a + b + c + 5)! possible orderings. It can be shown that this answer can always be expressed as a fraction frac{p}{q} where p and q are coprime integers. Output p cdot q^{-1} modulo 998 ,244 ,353 . The first line contains a single integer t ( 1 <= t <= 10^4 ) -- the number of test cases. Each test case contains three integers a , b , and c ( 0 <= a, b, c <= 2 cdot 10^5 ) xe2 x80 x93 the number of draw 0 cards, draw 1 cards, and draw 2 cards, respectively. It is guaranteed that the sum of a over all test cases does not exceed 2 cdot 10^5 , the sum of b over all test cases does not exceed 2 cdot 10^5 , and the sum of c over all test cases does not exceed 2 cdot 10^5 . For each test case, output a single integer -- the probability that Bessie wins, modulo 998 ,244 ,353 . In the first case, we have 1 of each type of "draw" card and 5 special cards. There are 30 ,720 starting decks where Bessie will win by drawing the top 5 '...