A Balanced Route Through the Grid

You are given an m × n grid grid where every cell holds a bracket, ( or ). A route starts at the top-left cell, ends at the bottom-right cell and moves either right or down at every step. Writing down the brackets of its cells in order gives a string. A bracket string is *balanced* if every opening bracket can be paired with a closing bracket after it so that the pairs do not cross: (())() is balanced, while )( and (() are not. Return True if some route produces a balanced string, and False otherwise.

grid=[['(', '(', ')'], [')', '(', ')']] → True

grid=[['(', '(', ')'], ['(', ')', '(']] → False

grid=[['(', ')', '('], [')', '(', ')'], ['(', ')', ')'], [')', '(', ')']] → True