Score : $300$ points

Problem Statement

Given are three positive integers $A$, $B$, and $C$. Compute the following value modulo $998244353$:

$\sum_{a=1}^{A} \sum_{b=1}^{B} \sum_{c=1}^{C} abc$

Constraints

• $1 \leq A, B, C \leq 10^9$

Input

Input is given from standard input in the following format:

$A$ $B$ $C$

Output

Print the value modulo $998244353$.

1 2 3

18

We have: $(1 \times 1 \times 1) + (1 \times 1 \times 2) + (1 \times 1 \times 3) + (1 \times 2 \times 1) + (1 \times 2 \times 2) + (1 \times 2 \times 3) = 1 + 2 + 3 + 2 + 4 + 6 = 18$.

1000000000 987654321 123456789

951633476

Be sure to compute the value modulo $998244353$.