Problem Statement

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.
Square $(i, j)$ has a non-negative integer $a_{i, j}$ written on it.

When 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.

Find 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 $0$.

What is the exclusive logical sum? The exclusive logical sum $a \\oplus b$ of two integers $a$ and $b$ is defined as follows.

• 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 $0$.

For example, $3 \\oplus 5 = 6$ (In binary notation: $011 \\oplus 101 = 110$).
In 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 $p_1, \\dots, p_k$.

Constraints

• $2 \\leq N \\leq 20$
• $0 \\leq a_{i, j} \\lt 2^{30} \\, (1 \\leq i, j \\leq N)$
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

$N$ $a_{1, 1}$ $\\ldots$ $a_{1, N}$ $\\vdots$ $a_{N, 1}$ $\\ldots$ $a_{N, N}$

Output

Print the answer.

Sample Input 1

3
1 5 2
7 0 5
4 2 3

Sample Output 1

2

The following two ways satisfy the condition:

• $(1, 1) \\rightarrow (1, 2) \\rightarrow (1, 3) \\rightarrow (2, 3) \\rightarrow (3, 3)$;
• $(1, 1) \\rightarrow (2, 1) \\rightarrow (2, 2) \\rightarrow (2, 3) \\rightarrow (3, 3)$.

Sample Input 2

2
1 2
2 1

Sample Output 2

0

Sample Input 3

10
1 0 1 0 0 1 0 0 0 1
0 0 0 1 0 1 0 1 1 0
1 0 0 0 1 0 1 0 0 0
0 1 0 0 0 1 1 0 0 1
0 0 1 1 0 1 1 0 1 0
1 0 0 0 1 0 0 1 1 0
1 1 1 0 0 0 1 1 0 0
0 1 1 0 0 1 1 0 1 0
1 0 1 1 0 0 0 0 0 0
1 0 1 1 0 0 1 1 1 0

Sample Output 3

24307