## Small Graphs Isomorphism

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^{}The score of an undirected simple graph (without self-loops) is a sequence of degrees of all its vertices sorted in non-increasing order.

**The task**

Find the number of all mutually non-isomorphic simple graphs with the given score.

### Input

Input consists of one text line containing at least two integers. The first integer N specifies the number of vertices of the graph. Integer N is followed by N other integers specifying the score of the graph. All integers are separarted by space. Value N is at least 2 and at at most 12 and the sum of all values in the score is at least 2.### Output

Output consists of one text line containing one integer equal to the number of all mutually non-isomorphic simple graphs with the given score. Output value is greater than 0 and it does not exceed 100.### Example 1

Input:6 3 3 2 2 2 2Output:

4

Fig. 1. All four non-isomorphic graphs with score 3, 3, 2, 2, 2, 2. |

### Example 2

Input:8 4 2 2 2 1 1 1 1Output:

7

Fig. 2. All seven non-isomorphic graphs with score 4, 2, 2, 2, 1, 1, 1, 1. |

### Example 3

Input:12 4 4 3 3 2 2 0 0 0 0 0 0Output:

5

Fig. 3. All five non-isomorphic graphs with score 4, 4, 3, 3, 2, 2, 0, 0, 0, 0, 0, 0. |