Problem Statement

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}

Output

Print $T$ lines. The $i$-th line should contain the answer for $\text{case}_{i}$.