Problem Statement

Snuke received an integer sequence $a$ of length $2N-1$.

He arbitrarily permuted the elements in $a$, then used it to construct a new integer sequence $b$ of length $N$, as follows:

• $b_1 =$ the median of $(a_1)$
• $b_2 =$ the median of $(a_1, a_2, a_3)$
• $b_3 =$ the median of $(a_1, a_2, a_3, a_4, a_5)$
• $:$
• $b_N =$ the median of $(a_1, a_2, a_3, ..., a_{2N-1})$

How many different sequences can be obtained as $b$? Find the count modulo $10^{9} + 7$.

Constraints

• $1 ≤ N ≤ 50$
• $1 ≤ a_i ≤ 2N-1$
• $a_i$ are integers.

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_{2N-1}

Output

Print the answer.