You are given an m x n grid grid where: '.' is an empty cell. '#' is a wall. '@' is the starting point. Lowercase letters represent keys. Uppercase letters represent locks. You start at the starting point and one move consists of walking one space in one of the four cardinal directions. You cannot walk outside the grid, or walk into a wall. If you walk over a key, you can pick it up and you cannot walk over a lock unless you have its corresponding key. For some 1 <= k <= 6, there is exactly one lowercase and one uppercase letter of the first k letters of the English alphabet in the grid.