Score : $1600$ points

Problem Statement

There is a sequence of length $2N$: $A_1, A_2, ..., A_{2N}$. Each $A_i$ is either $-1$ or an integer between $1$ and $2N$ (inclusive). Any integer other than $-1$ appears at most once in ${A_i}$.

For each $i$ such that $A_i = -1$, Snuke replaces $A_i$ with an integer between $1$ and $2N$ (inclusive), so that ${A_i}$ will be a permutation of $1, 2, ..., 2N$. Then, he finds a sequence of length $N$, $B_1, B_2, ..., B_N$, as $B_i = min(A_{2i-1}, A_{2i})$.

Find the number of different sequences that $B_1, B_2, ..., B_N$ can be, modulo $10^9 + 7$.

Constraints

• $1 \leq N \leq 300$
• $A_i = -1$ or $1 \leq A_i \leq 2N$.
• If $A_i \neq -1, A_j \neq -1$, then $A_i \neq A_j$. ($i \neq j$)

Input

Input is given from Standard Input in the following format:

$N$

$A_1$ $A_2$ $...$ $A_{2N}$

Output

Print the number of different sequences that $B_1, B_2, ..., B_N$ can be, modulo $10^9 + 7$.

3
1 -1 -1 3 6 -1

5

There are six ways to make ${A_i}$ a permutation of $1, 2, ..., 2N$; for each of them, ${B_i}$ would be as follows:

• $(A_1, A_2, A_3, A_4, A_5, A_6) = (1, 2, 4, 3, 6, 5)$: $(B_1, B_2, B_3) = (1, 3, 5)$
• $(A_1, A_2, A_3, A_4, A_5, A_6) = (1, 2, 5, 3, 6, 4)$: $(B_1, B_2, B_3) = (1, 3, 4)$
• $(A_1, A_2, A_3, A_4, A_5, A_6) = (1, 4, 2, 3, 6, 5)$: $(B_1, B_2, B_3) = (1, 2, 5)$
• $(A_1, A_2, A_3, A_4, A_5, A_6) = (1, 4, 5, 3, 6, 2)$: $(B_1, B_2, B_3) = (1, 3, 2)$
• $(A_1, A_2, A_3, A_4, A_5, A_6) = (1, 5, 2, 3, 6, 4)$: $(B_1, B_2, B_3) = (1, 2, 4)$
• $(A_1, A_2, A_3, A_4, A_5, A_6) = (1, 5, 4, 3, 6, 2)$: $(B_1, B_2, B_3) = (1, 3, 2)$

Thus, there are five different sequences that $B_1, B_2, B_3$ can be.

4
7 1 8 3 5 2 6 4

1

10
7 -1 -1 -1 -1 -1 -1 6 14 12 13 -1 15 -1 -1 -1 -1 20 -1 -1

9540576

20
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 6 -1 -1 -1 -1 -1 7 -1 -1 -1 -1 -1 -1 -1 -1 -1 34 -1 -1 -1 -1 31 -1 -1 -1 -1 -1 -1 -1 -1

374984201