Problem:


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.

Sample Input 1

3
1 -1 -1 3 6 -1

Sample Output 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.

Sample Input 2

4
7 1 8 3 5 2 6 4

Sample Output 2

1

Sample Input 3

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

Sample Output 3

9540576

Sample Input 4

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

Sample Output 4

374984201



Sample input:
3
1 -1 -1 3 6 -1


Sample output:
5

Submission status: Runtime Error

Solution code:
n = int(input())
a = [int(i) for i in input().split()]
b = []
d = []
for i in range(len(a)):
  b.append(a[2*i]-a[2*i+1])
c = [i for i in a.split() if i != '-1']
c = list(set(range(1,len(a)+1) ^ set(c)))
for i in range(len(b)):
  if b[i]-1 == a[2*i]:
    d.append([i for i in c if i < a[2*i]] + [a[2*i]])
  elif b[i]+a[2*i] == -1:
    d.append([i for i in c if i < a[2*i+1]] + [a[2*i]+1])
  elif b[i] == 0:
    d.append([i for i in c if i != max(c)])
f = 1
for i in d:
  f *= len(i)
for i in range(len(c)):
  if [e for i in d for e in i].count(c[i]) >= 2:
    g = 1
    for j in d:
      g *= len(j)-j.count(c[i])
    f -= g
print(f)

Submission status: Runtime Error

Solution code:
n = int(input())
a = [int(i) for i in input().split()]
b = []
d = []
for i in range(len(a)):
  b.append(a[2i]-a[2i+1])
c = [i for i in a.split() if i != '-1']
c = list(set(range(1,len(a)+1) ^ set(c))
for i in range(len(b)):
  if b[i]-1 == a[2*i]:
    d.append([i for i in c if i < a[2*i]] + [a[2*i]])
  elif b[i]+a[2*i] == -1:
    d.append([i for i in c if i < a[2*i+1]] + [a[2*i]+1])
  elif b[i] == 0:
    d.append([i for i in c if i != max(c)])
f = 1
for i in d:
  f *= len(i)
for i in range(len(c)):
  if [e for i in d for e in i].count(c[i]) >= 2:
    g = 1
    for j in d:
      g *= len(j)-j.count(c[i])
    f -= g
print(f)