Description

The cows are playing a non-traditional version of the children's "hopscotch" game. Instead of a linear arrangement of numbered squares, they have created a $5 \times 5$ grid of numbers, aligned with the $x$ and $y$ axes. The cows skillfully jump from number to number in the grid: forward, backward, left, or right (never diagonally), landing on another number in the grid. They continue jumping (using the same rules), possibly landing on numbers they've already visited. After a total of five jumps, their path forms a six-digit integer (which may start with $0$, e.g., $000201$). Find the total number of distinct integers that can be formed in this way.

Input Format

Lines $1$ to $5$: The grid, each line contains $5$ integers.

Output Format

Line $1$: The total number of distinct integers that can be formed.

Sample

1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 2 1
1 1 1 1 1

15