Solve the programming task below in a Python markdown code block.
You are given three positive integers N, x, and y.

Count the number of arrays P of length N such that:
P_{1} = P_{N} = 1
There are exactly x indices i such that P_{i}=1
There are exactly y indices i such that P_{i}=2
There are exactly N-x-y indices i such that P_{i}=3
P_{i} \neq P_{i+1} for each 1 ≤ i < N

Since the answer can be large, output it modulo 998244353.

------ Input Format ------ 

- The first and only line of input will contain three space-separated integers N, x and y.

------ Output Format ------ 

Output a single integer: the number of arrays obtained, modulo 998244353.

------ Constraints ------ 

$3 ≤ N ≤ 2 \cdot 10^{6}$
$2 ≤ x ≤ N-1$
$1 ≤ y ≤ N-2$
$x + y ≤ N$

----- Sample Input 1 ------ 
5 3 1

----- Sample Output 1 ------ 
2
----- explanation 1 ------ 

----- Sample Input 2 ------ 
10 4 3

----- Sample Output 2 ------ 
44
----- explanation 2 ------ 
Test case $1$: Only two valid arrays are possible: 
- $[1,2,1,3,1]$
- $[1,3,1,2,1]$

Test case $2$: A couple of valid arrays are $[1, 2, 3, 1, 2 ,3, 1, 2, 3, 1]$ and $[1, 3, 2, 1, 3, 1, 2, 3, 2, 1]$. It can be verified that there are $44$ in total.