<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)
        a, b = 0, 0
        found = False
        for i in range(n):
            for j in range(n):
                if grid[i][j] == 1:
                    a, b = i, j
                    found = True
                    break
            if found:
                break
        island1 = [ [ False for _ in range(n) ] for _ in range(n) ]
        island1[i][j] = True
        water = deque()
        waterSeen = [ [ False for _ in range(n) ] for _ in range(n) ]
        q = deque()
        q.append((i,j))
        dd = ((1,0), (0,1), (-1,0), (0,-1))
        while q:
            x, y = q.popleft()
            for dx, dy in dd:
                xx = x + dx
                yy = y + dy
                if xx >= 0 and xx < n and yy >= 0 and yy < n:
                    if grid[xx][yy] == 0:
                        water.append((xx,yy))
                        waterSeen[xx][yy] = True
                    elif not island1[xx][yy]:
                        island1[xx][yy] = True
                        q.append((xx,yy))
        c = 0
        while water:
            m = len(water)
            c += 1
            for k in range(m):
                x, y = water.popleft()
                for dx, dy in dd:
                    xx = x + dx
                    yy = y + dy
                    if xx >= 0 and xx < n and yy >= 0 and yy < n:
                        if grid[xx][yy] == 1:
                            if not island1[xx][yy]:
                                return c
                        else:
                            if not waterSeen[xx][yy]:
                                waterSeen[xx][yy] = True
                                water.append((xx,yy))
        return 0
16800