Problem Statement

There are $2$ countries, the yuki country and the coder country, which have different cultures regarding colors. Because of this cultural difference, these $2$ countries are characterized by describing the color of even the same object differently.

Also, because of the cultural difference, the colors that make up a rainbow differ between the yuki country and the coder country.

Specifically, in the yuki country a rainbow consists of the $M$ colors $1, 2, \dots, M$, and in the coder country a rainbow consists of the $L$ colors $M + 1, M + 2, \dots, M + L$.

There are $N$ pens here. The $i$-th pen has color $A_i(1 \leq A_i \leq M)$ in the yuki country and color $B_i(M + 1 \leq B_i \leq M + L)$ in the coder country.

Note that there is no correspondence of colors between the $2$ countries across different pens. (For distinct $i, j$, even if $A_i = A_j$, it is not necessarily the case that $B_i = B_j$.)

There are $2^N - 1$ ways to choose at least $1$ of the $N$ pens. Among them, find the number of ways that satisfy the following condition.

• For both the yuki country and the coder country, the chosen pens include all the colors that make up a rainbow in that country.

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

Constraints

• All inputs are integers.
• $1 \leq N \leq 2 \times 10^5$
• $1 \leq M, L \leq 18$
• $1 \leq A_i \leq M$
• $M + 1 \leq B_i \leq M + L$

Input

The input is given from Standard Input in the following format.

$N$ $M$ $L$
$A_1$ $B_1$
$A_2$ $B_2$
$\vdots$
$A_N$ $B_N$

Output

Output the number of ways to choose pens satisfying the condition, modulo $998244353$.

Sample

4 2 2
1 3
1 4
2 3
2 4

7

2 2 2
1 3
1 3

0

12 3 4
1 5
2 5
2 4
1 6
3 7
3 4
2 6
1 4
2 7
1 7
3 5
3 6

2161