Two-Sided Skyline Tour

Time limit: 4000 msMemory limit: 256 MB

Along a west-to-east trail stand $N$ observation towers. Their distinct heights are $A_1, A_2, \ldots, A_N$ .

A tour is formed by choosing a nonempty subsequence of towers. More precisely, a tour chooses indices

$1 \le i_1 < i_2 < \ldots < i_M \le N.$

The chosen tower at index $i_t$ is a west-record if it is taller than every tower chosen before it. That is, $A_{i_t} > A_{i_s}$ for every . The first chosen tower is always a west-record.

The chosen tower at index $i_t$ is an east-record if it is taller than every tower chosen after it. That is, $A_{i_t} > A_{i_s}$ for every . The last chosen tower is always an east-record.

A chosen tower may be both a west-record and an east-record. Two tours are distinct if their chosen index sequences are different.

Count the tours containing exactly $P$ west-records and exactly $Q$ east-records. Since the answer can be large, report it modulo $998244353$ .

Input

The first line contains three integers $N$ , $P$ , and $Q$ , where $N$ is the number of towers, $P$ is the required number of west-records, and $Q$ is the required number of east-records.

Output

Print one integer: the number of tours having exactly $P$ west-records and exactly $Q$ east-records, modulo $998244353$ .

Samples

Sample 1

Input

4 2 1
2 4 1 3

Output

The valid tours have index sequences $(1,2)$ , $(1,4)$ , $(3,4)$ , and $(1,3,4)$ .

Two-Sided Skyline Tour

Input

Output

Samples

Sample 1

Submit

Submissions

Sample 2

Sample 3