Problem Description

Given a $n \times n \times n$ cube divided into $n^3$ unit cubes, some of which are obstacles and cannot be traversed.

Given the starting coordinates and the destination coordinates, each step allows moving from one unit cube to an adjacent (sharing a face) non-obstacle unit cube. Determine the minimum number of steps required to travel from the start to the destination.

Input Format

The first line contains an integer $n$.

The next line contains three integers $x_s, y_s, z_s$ representing the starting position.

The following line contains three integers $x_t, y_t, z_t$ representing the destination position.

Next, $n$ $n \times n$ matrices of $0$s and $1$s are provided, where the $i$-th matrix's $j$-th row and $k$-th column indicate whether $(j, k, i)$ is an obstacle (1 indicates an obstacle).

It is guaranteed that the starting and destination positions are not obstacles.

Output Format

Output a single integer representing the minimum number of steps. If it is not possible to reach the destination, output $-1$.

Sample Input and Output

Sample Input #1

2
1 1 1
1 1 2
00
10
01
00

Sample Output #1

1

Sample Input #2

3
2 3 1
1 1 1
000
010
000
111
111
111
111
111
111

Sample Output #2

3

Sample Input #3

3
2 1 1
3 2 2
000
010
110
010
001
001
101
110
000

Sample Output #3

3

Notes

Data Range

For all data, $1 \le n \le 100$.

见题面 Input 部分

见题面 Output 部分