Problem Statement

There is a blackboard with a set of positive integers written on it. Initially, the set $S=\lbrace 1,2,\dots,A,A+1,A+2,\dots,A+B\rbrace$ is written on the blackboard.
Takahashi wants to perform the following operation N-1 times to have N sets on the blackboard:

• From the sets of integers written on the blackboard, choose a set S_0 that contains at least one element not greater than A and at least one element not less than A+1. From the chosen set S_0, choose one element a not greater than A and one element b not less than A+1. Erase the set S_0 from the blackboard and write two sets S_1 and S_2 of his choice that satisfy all of the following conditions:
• The union of S_1 and S_2 is S_0, and they have no common elements.
• $a \in$ $S_1, b \in$ S_2

Find the number of possible ways to perform the series of operations, modulo 998244353.
Here, two series of operations are distinguished when there is an i\ $(1 \leq i \leq N-1)$ such that S_0, a, b, S_1, or S_2 chosen in the i-th operation of one series is different from that of the other series.

Input

The input is given from Standard Input in the following format:
N A B

Output

Print the answer.

Constraints

• $2 \leq N \leq 2 \times 10^5$
• $1 \leq A,B \leq 2 \times 10^5$
• $N \leq A+B$
• All input values are integers.

Sample Input 1

3 2 4

Sample Output 1

1728

One possible series of operations is as follows:

• Choose $S_0=\lbrace 1,2,3,4,5,6\rbrace$, let a=2 and b=5, and let $S_1 =\lbrace 1,2,3,6\rbrace$ and $S_2=\lbrace 4,5\rbrace.$ There are now two sets of integers written on the blackboard: $\lbrace 1,2,3,6\rbrace$ and $\lbrace 4,5\rbrace$.
• Choose $S_0=\lbrace 1,2,3,6\rbrace$, let a=1 and b=3, and let $S_1 = \lbrace1,2\rbrace$ and $S_2=\lbrace 3,6\rbrace.$ There are now three sets of integers written on the blackboard: $\lbrace 1,2\rbrace, \lbrace 3,6\rbrace$, and $\lbrace 4,5\rbrace$.

Sample Input 2

4 1 3

Sample Output 2

6

If we let a=1 and b=2 and let $S_1 = \lbrace 1\rbrace$ and $S_2 = \lbrace 2,3,4\rbrace$ in the first operation, we can no longer perform the second and subsequent operations.
Do not count these cases where we cannot complete N-1 operations.

Sample Input 3

5 6 6

Sample Output 3

84486693

Sample Input 4

173173 173173 173173

Sample Output 4

446948086

见题面 Input 部分

见题面 Output 部分