Problem Statement

You are given integers $A$, $B$, and $C$. How many strings $S$ consisting of A, B, and C satisfy all of the following conditions? Find the count modulo $998244353$.

• The number of occurrences of A, B, and C in $S$ are $A$, $B$, and $C$, respectively.
• $S$ contains none of ABC, BCA, and CAB as a (contiguous) substring.

Constraints

• $1 \\leq A,B,C \\leq 10^6$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$A$ $B$ $C$

Output

Print the answer.

Sample Input 1

1 1 1

Sample Output 1

3

The three strings that satisfy the conditions are ACB, CBA, and BAC.

Sample Input 2

2 2 2

Sample Output 2

42

Sample Input 3

96 11 46

Sample Output 3

818015722

Sample Input 4

125132 102271 152064

Sample Output 4

128086069