1 + 6 = 7

AtCoder

IDarc178_b

Time2000ms

Memory256MB

Difficulty—

You are given positive integers $A_{1}, A_{2}, A_{3}$. Find the number, modulo $998244353$, of tuples of positive integers $(X_{1}, X_{2}, X_{3})$ that satisfy all of the following conditions. * $X_{1}$ is a positive integer with $A_{1}$ digits in decimal notation. * $X_{2}$ is a positive integer with $A_{2}$ digits in decimal notation. * $X_{3}$ is a positive integer with $A_{3}$ digits in decimal notation. * $X_{1} + X_{2} = X_{3}$. You are given $T$ test cases per input file; solve each of them. ## Constraints * $1 \leq T \leq 10^{5}$ * $1 \leq A_{i} \leq 10^{9}$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $T$ $\text{case}_{1}$ $\text{case}_{2}$ $\vdots$ $\text{case}_{T}$ Each case is given in the following format: $A_{1}$ $A_{2}$ $A_{3}$ [samples]

Samples

Input #1

4
1 1 1
1 6 7
167 167 167
111 666 777

Output #1

36
45
731780675
0

For the first case, tuples such as $(X_{1}, X_{2}, X_{3}) = (1, 6, 7), (2, 1, 3)$ satisfy the conditions.
On the other hand, tuples such as $(X_{1}, X_{2}, X_{3}) = (6, 7, 13), (3, 4, 5)$ do not.
There are $36$ tuples $(X_{1}, X_{2}, X_{3})$ that satisfy the conditions, so print $36$.
For the third case, remember to print the result modulo $998244353$.
For the fourth case, there may be no tuples $(X_{1}, X_{2}, X_{3})$ that satisfy the conditions.

API Response (JSON)

{
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      "content": "You are given positive integers $A_{1}, A_{2}, A_{3}$. Find the number, modulo $998244353$, of tuples of positive integers $(X_{1}, X_{2}, X_{3})$ that satisfy all of the following conditions. *   $X",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
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    "difficulty": "None",
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    "sync_url": null,
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  "statements": [
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      "statement_type": "Markdown",
      "content": "You are given positive integers $A_{1}, A_{2}, A_{3}$. Find the number, modulo $998244353$, of tuples of positive integers $(X_{1}, X_{2}, X_{3})$ that satisfy all of the following conditions.\n\n*   $X...",
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      "language": "English"
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Full JSON Raw Segments