Hexagonal Grid: Distance

A hexagonal grid is a commonly used game board design based on hexagonal tiling. In the following grid, the two marked locations have a minimum distance of 6 because at least 6 steps are needed to reach the second location starting from the first one.

Write a function that takes a hexagonal grid with two marked locations as input and returns their distance.

The input grid will be a list of strings in which each tile is represented with o and the two marked locations with x.

Examples

hex_distance([
  "  o o  ",
  " o x o ",
  "  o x  ",
]) ➞ 1

hex_distance([
  "  o o  ",
  " x o o ",
  "  o x  ",
]) ➞ 2

hex_distance([
  "   o o o   ",
  "  o o o o  ",
  " o o o o o ",
  "  x o o x  ",
  "   o o o   ",
]) ➞ 3

Notes

N/A