Volcano has $n$ sets, where the $i$-th set initially contains only one number $a_i$. In each step, Volcano chooses two sets uniformly at random and merges them into one. Volcano repeats this process until exactly $k$ sets remain.

Let the final sets be $S_1, \dots, S_k$. Let $max(T)$ and $min(T)$ denote the maximum and minimum values in a set $T$, respectively. Volcano receives a reward of $\sum_{i=1}^{k}(max(S_i)-min(S_i))^2$.

Let $f(k)$ be the expected reward when exactly $k$ sets remain. To reduce the output size, you only need to output the value of $\sum_{k=l}^{r}f(k)^{97376}$ modulo $998244353$.

We define the value of a fraction $a/b$ modulo $998244353$ as $c$ if and only if $(b\times c) \pmod{998244353} = a$, where $0 \leq c < 998244353$.

Input

The first line contains three positive integers $n, l, r$.

The second line contains $n$ integers representing $a_i$.

Output

Output a single number representing the required answer.

Examples

Input 1

3 1 3
1 2 3

Output 1

686489728

Input 2

13 1 13
1 1 4 5 1 4 1 9 1 9 8 1 0

Output 2

430310636

Subtasks

Task 1 (1 pt): $l=r=1$

Task 2 (9 pts): $1\leq n\leq 7$

Task 3 (8 pts): $l=r=n-1$

Task 4 (11 pts): $1\leq n\leq 100$

Task 5 (21 pts): $1\leq n\leq 2000$

Task 6 (13 pts): $l=r$

Task 7 (37 pts): No special constraints

For all data, $1\leq n\leq 2\times 10^5$, $0\leq a_i < 998244353$, and $1\leq l\leq r\leq n$.