The Shortest Path

Given a rectangular grid of m by n spaces, signaled by 0s, and a number of points, signaled by 1, 2, 3..., return the number of moves for the shortest path that starts at 1 and goes over all the other points in ascending order.

Examples

shortest_path([
  ("001"),
  ("002"),
  ("003")
]) ➞ 2

shortest_path([
  ("00000"),
  ("01006"),
  ("02000"),
  ("30050"),
  ("00004")
]) ➞ 13

shortest_path([
  ("00020000"),
  ("01000000")
]) ➞ 3

Notes

• Only horizontal and vertical movements are allowed.
• All movements from one place to an adjacent one count as 1 regardless of direction.
• The points range from 1 to at most 9 with no repeating or missing digits.