{"raw_statement":[{"iden":"problem statement","content":"You are given a sequence of integers $(X_1,\\dots,X_M)$ of length $M$ consisting of $1,\\dots,K$.\nFind the number of sequences $(A_1,\\dots,A_N)$ of length $N$ consisting of $1,\\dots,K$ that satisfy the following condition, modulo $998244353$:\n\n*   Among all sequences of length $M$ consisting of $1,\\dots,K$, the only sequence that cannot be obtained as a (not necessarily contiguous) subsequence of $(A_1,\\dots,A_N)$ is $(X_1,\\dots,X_M)$."},{"iden":"constraints","content":"*   $2\\le M,K \\le N \\le 400$\n*   $1\\le X_i \\le K$\n*   All input values are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$ $M$ $K$\n$X_1$ $X_2$ $\\dots$ $X_M$"},{"iden":"sample input 1","content":"5 2 3\n1 1"},{"iden":"sample output 1","content":"4\n\nThe following four sequences satisfy the condition:\n\n*   $(2, 3, 1, 2, 3)$\n*   $(2, 3, 1, 3, 2)$\n*   $(3, 2, 1, 2, 3)$\n*   $(3, 2, 1, 3, 2)$"},{"iden":"sample input 2","content":"400 3 9\n1 8 6"},{"iden":"sample output 2","content":"417833302"},{"iden":"sample input 3","content":"29 3 10\n3 3 3"},{"iden":"sample output 3","content":"495293602"},{"iden":"sample input 4","content":"29 3 10\n3 3 4"},{"iden":"sample output 4","content":"0"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}