<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:
        visited = set()
        ROW = len(grid)
        COL = len(grid[0])
        ret = float("inf")

        def dfs(r,c):
            if r < 0 or r == ROW or c < 0 or c == COL or (r,c) in visited or grid[r][c] == 0:
                return
            visited.add((r,c))
            grid[r][c] = 2
            move = [[-1,0],[1,0],[0,-1],[0,1]]

            for x,y in move:
                dfs(r+x,c+y)
        
        loop = False
        for r in range(ROW):
            for c in range(COL):
                if grid[r][c] == 1:
                    dfs(r,c)
                    loop = True
                    break
            if loop:
                break
        q = collections.deque(visited)
        ret = 0
        seen = set()
        while q:
            snapshot = len(q)
            for i in range(snapshot):
                r, c = q.popleft()
                if grid[r][c] == 1:
                    return ret
                move = [[-1,0],[1,0],[0,-1],[0,1]]
                for x,y in move:
                    r1 = r + x
                    c1 = c + y
                    if r1 >= 0 and r1 < ROW and c1 >= 0 and c1 < COL and grid[r1][c1] != 2:
                        if grid[r1][c1] == 1: return ret
                        q.append((r1,c1))
                        grid[r1][c1] = 2
            ret += 1
        return -1


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