Score : $1600$ points
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 $10^9 + 7$.
Input is given from Standard Input in the following format:
$N$ $A_1$ $A_2$ $...$ $A_{2N}$
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:
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