You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 256.0 MB

# Problem
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 $$$998\,244\,353$$$.

## Input Format
The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.

Each test case contains three integers $$$a$$$, $$$b$$$, and $$$c$$$ ($$$0 \le a, b, c \le 2 \cdot 10^5$$$) – 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 $$$2 \cdot 10^5$$$.

## Output Format
For each test case, output a single integer — the probability that Bessie wins, modulo $$$998\,244\,353$$$.

## Examples
```input
4
1 1 1
0 0 0
5 3 7
3366 1434 1234
```
```output
903173463
1
35118742
398952013
```

## Note
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 $$$5$$$ cards and $$$40\,320$$$ starting decks in total. Thus, the probability of Bessie winning is $$$\frac{30\,720}{40\,320} = \frac{16}{21}$$$.

One example of a winning starting deck is, top to bottom,

1. "Special",
2. "Draw $$$1$$$",
3. "Special",
4. "Special",
5. "Draw $$$0$$$",
6. "Draw $$$2$$$",
7. "Special",
8. "Special".

One example of a losing starting deck is:

1. "Special",
2. "Draw $$$1$$$",
3. "Special",
4. "Special",
5. "Draw $$$0$$$",
6. "Special",
7. "Special",
8. "Draw $$$2$$$".

Now solve the problem and return the code.