{"raw_statement":[{"iden":"problem statement","content":"There is a grid with $N$ rows and $N$ columns. We denote by $(i, j)$ the square at the $i$\\-th $(1 \\leq i \\leq N)$ row from the top and $j$\\-th $(1 \\leq j \\leq N)$ column from the left.  \nSquare $(i, j)$ has a non-negative integer $a_{i, j}$ written on it.\nWhen you are at square $(i, j)$, you can move to either square $(i+1, j)$ or $(i, j+1)$. Here, you are not allowed to go outside the grid.\nFind the number of ways to travel from square $(1, 1)$ to square $(N, N)$ such that the exclusive logical sum of the integers written on the squares visited (including $(1, 1)$ and $(N, N)$) is $0$.\nWhat is the exclusive logical sum? The exclusive logical sum $a \\oplus b$ of two integers $a$ and $b$ is defined as follows.\n\n*   The $2^k$'s place ($k \\geq 0$) in the binary notation of $a \\oplus b$ is $1$ if exactly one of the $2^k$'s places in the binary notation of $a$ and $b$ is $1$; otherwise, it is $0$.\n\nFor example, $3 \\oplus 5 = 6$ (In binary notation: $011 \\oplus 101 = 110$).  \nIn general, the exclusive logical sum of $k$ integers $p_1, \\dots, p_k$ is defined as $(\\cdots ((p_1 \\oplus p_2) \\oplus p_3) \\oplus \\cdots \\oplus p_k)$. We can prove that it is independent of the order of $p_1, \\dots, p_k$."},{"iden":"constraints","content":"*   $2 \\leq N \\leq 20$\n*   $0 \\leq a_{i, j} \\lt 2^{30} \\, (1 \\leq i, j \\leq N)$\n*   All values in the input are integers."},{"iden":"input","content":"The 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":"3\n1 5 2\n7 0 5\n4 2 3"},{"iden":"sample output 1","content":"2\n\nThe following two ways satisfy the condition:\n\n*   $(1, 1) \\rightarrow (1, 2) \\rightarrow (1, 3) \\rightarrow (2, 3) \\rightarrow (3, 3)$;\n*   $(1, 1) \\rightarrow (2, 1) \\rightarrow (2, 2) \\rightarrow (2, 3) \\rightarrow (3, 3)$."},{"iden":"sample input 2","content":"2\n1 2\n2 1"},{"iden":"sample output 2","content":"0"},{"iden":"sample input 3","content":"10\n1 0 1 0 0 1 0 0 0 1\n0 0 0 1 0 1 0 1 1 0\n1 0 0 0 1 0 1 0 0 0\n0 1 0 0 0 1 1 0 0 1\n0 0 1 1 0 1 1 0 1 0\n1 0 0 0 1 0 0 1 1 0\n1 1 1 0 0 0 1 1 0 0\n0 1 1 0 0 1 1 0 1 0\n1 0 1 1 0 0 0 0 0 0\n1 0 1 1 0 0 1 1 1 0"},{"iden":"sample output 3","content":"24307"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}