{"raw_statement":[{"iden":"problem statement","content":"Snuke received an integer sequence $a$ of length $2N-1$.\nHe arbitrarily permuted the elements in $a$, then used it to construct a new integer sequence $b$ of length $N$, as follows:\n\n*   $b_1 =$ the median of $(a_1)$\n*   $b_2 =$ the median of $(a_1, a_2, a_3)$\n*   $b_3 =$ the median of $(a_1, a_2, a_3, a_4, a_5)$\n*   $:$\n*   $b_N =$ the median of $(a_1, a_2, a_3, ..., a_{2N-1})$\n\nHow many different sequences can be obtained as $b$? Find the count modulo $10^{9} + 7$."},{"iden":"constraints","content":"*   $1 ≤ N ≤ 50$\n*   $1 ≤ a_i ≤ 2N-1$\n*   $a_i$ are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$\n$a_1$ $a_2$ $...$ $a_{2N-1}$"},{"iden":"sample input 1","content":"2\n1 3 2"},{"iden":"sample output 1","content":"3\n\nThere are three sequences that can be obtained as $b$: $(1,2)$, $(2,2)$ and $(3,2)$. Each of these can be constructed from $(1,2,3)$, $(2,1,3)$ and $(3,1,2)$, respectively."},{"iden":"sample input 2","content":"4\n1 3 2 3 2 4 3"},{"iden":"sample output 2","content":"16"},{"iden":"sample input 3","content":"15\n1 5 9 11 1 19 17 18 20 1 14 3 3 8 19 15 16 29 10 2 4 13 6 12 7 15 16 1 1"},{"iden":"sample output 3","content":"911828634\n\nPrint the count modulo $10^{9} + 7$."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}