{"raw_statement":[{"iden":"problem statement","content":"We have a grid of squares with $N$ rows arranged vertically and $N$ columns arranged horizontally. The square at the $i$\\-th row from the top and $j$\\-th column from the left has an integer label $a_{i,j}$.  \nConsider paths obtained by starting on one of the squares and going **right or down** to an adjacent square zero or more times. Find the number, modulo $998244353$, of such paths that start and end on squares with the same label.  \nTwo paths are distinguished when they visit different sets of squares (including the starting and ending squares)."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 400$\n*   $1 \\leq a_{i,j} \\leq N^2$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$\n$a_{1,1}$ $\\ldots$ $a_{1,N}$\n$\\vdots$\n$a_{N,1}$ $\\ldots$ $a_{N,N}$"},{"iden":"sample input 1","content":"2\n1 3\n3 1"},{"iden":"sample output 1","content":"6\n\nThe following six paths satisfy the requirements. ($(i, j)$ denotes the square at the $i$\\-th row from the top and $j$\\-th column from the left. Each path is represented as a sequence of squares it visits.)\n\n*   $(1,1)$\n*   $(1,1)$ → $(1,2)$ → $(2,2)$\n*   $(1,1)$ → $(2,1)$ → $(2,2)$\n*   $(1,2)$\n*   $(2,1)$\n*   $(2,2)$"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}