Score : 1000 points

Problem Statement

Snuke has come up with the following problem.

You are given a sequence d of length N. Find the number of the undirected graphs with N vertices labeled 1,2,...,N satisfying the following conditions, modulo 10^{9} + 7:

  • The graph is simple and connected.
  • The degree of Vertex i is d_i.

When 2 \leq N, 1 \leq d_i \leq N-1, {\rm Σ} d_i = 2(N-1), it can be proved that the answer to the problem is \frac{(N-2)!}{(d_{1} -1)!(d_{2} - 1)! ... (d_{N}-1)!}.

Snuke is wondering what the answer is when 3 \leq N, 1 \leq d_i \leq N-1, { \rm Σ} d_i = 2N. Solve the problem under this condition for him.

Constraints

  • 3 \leq N \leq 300
  • 1 \leq d_i \leq N-1
  • { \rm Σ} d_i = 2N

Partial Scores

  • In the test set worth 200 points, N \leq 5.
  • In the test set worth another 200 points, N \leq 18.
  • In the test set worth another 300 points, N \leq 50.

Input

Input is given from Standard Input in the following format:

N
d_1 d_2 ... d_{N}

Output

Print the answer.

Sample Input 1

5
1 2 2 3 2

Sample Output 1

6
  • There are six graphs as shown below:
51367cdb21c64bfb07113b300921d52c.png

Sample Input 2

16
2 1 3 1 2 1 4 1 1 2 1 1 3 2 4 3

Sample Output 2

555275958
  • Be sure to find the answer modulo 10^{9} + 7.