We are given an $n×n$ binary matrix grid containing 0s and 1s. Each cell in the grid represents either land or water. A cell with a value of 1 represents land, while a cell with a value of 0 represents water. A group of adjacent cells with a value of 1 constitutes an island. Two cells are considered adjacent if one is above, below, to the left, or to the right of the other. Our task is to return the smallest number of 0s we must flip to connect the two islands.

Note: We may assume all four edges of the grid are surrounded by water.

Constraints:

• $2$ $\leq$ n $\leq$ $20$

• $n ==$ grid.length $==$ grid[i].length.

• grid[i][j] is either 0 or 1.

• There are exactly two islands in the grid.

Let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps us to check if you’re solving the correct problem:

Implement your solution in the following coding playground: