<p>You are given an <code>n x n</code> binary matrix <code>grid</code> where <code>1</code> represents land and <code>0</code> represents water.</p>

<p>An <strong>island</strong> is a 4-directionally connected group of <code>1</code>&#39;s not connected to any other <code>1</code>&#39;s. There are <strong>exactly two islands</strong> in <code>grid</code>.</p>

<p>You may change <code>0</code>&#39;s to <code>1</code>&#39;s to connect the two islands to form <strong>one island</strong>.</p>

<p>Return <em>the smallest number of </em><code>0</code><em>&#39;s you must flip to connect the two islands</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> grid = [[0,1],[1,0]]
<strong>Output:</strong> 1
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> grid = [[0,1,0],[0,0,0],[0,0,1]]
<strong>Output:</strong> 2
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> grid = [[1,1,1,1,1],[1,0,0,0,1],[1,0,1,0,1],[1,0,0,0,1],[1,1,1,1,1]]
<strong>Output:</strong> 1
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>n == grid.length == grid[i].length</code></li>
	<li><code>2 &lt;= n &lt;= 100</code></li>
	<li><code>grid[i][j]</code> is either <code>0</code> or <code>1</code>.</li>
	<li>There are exactly two islands in <code>grid</code>.</li>
</ul>

class Solution:
    def shortestBridge(self, grid: List[List[int]]) -> int:
        n = len(grid)
        directions = [(0, 1), (0, -1), (1, 0), (-1, 0)]

        def valid(row, col):
            return row >= 0 and col >= 0 and row < len(grid) and col < len(grid[0])

        queue = deque([])
        def mark_group(row, col):
            grid[row][col] = "m"
            for d in directions:
                next_row, next_col = row + d[0], col + d[1]
                if valid(next_row, next_col):
                    if grid[next_row][next_col] == 0:
                        queue.append((row, col))
                    if grid[next_row][next_col] == 1:
                        mark_group(next_row, next_col)

        def mark_first_group():
            for row in range(n):
                for col in range(n):
                    if grid[row][col] == 1:
                        mark_group(row, col)
                        return

        mark_first_group()

        result = 0
        while queue:
            for _ in range(len(queue)):
                row, col = queue.popleft()

                for d in directions:
                    next_row, next_col = row + d[0], col + d[1]

                    if valid(next_row, next_col):
                        if grid[next_row][next_col] == 0:
                            grid[next_row][next_col] = "v"
                            queue.append((next_row, next_col))
                        elif grid[next_row][next_col] == 1:
                            return result
            result += 1
        return result


                    

    


        
        
        
        
18000