<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:
        def idfs(r,c):
            if r<0 or c<0 or r>=len(grid) or c>=len(grid[0]) or (r,c) in visited or grid[r][c] == 0: return
            visited.add((r,c))
            island1.append((r,c))
            grid[r][c] = -1
            idfs(r+1,c)
            idfs(r-1,c)
            idfs(r,c+1)
            idfs(r,c-1)
        def mark1():
            for row in range(len(grid)):
                for col in range(len(grid[0])):
                    if grid[row][col] == 1:
                        idfs(row,col)
                        return
        visited = set()
        island1 = deque()
        mark1()
        res = 0

        while island1:
            for _ in range(len(island1)):
                r,c = island1.popleft()
                for dr,dc in [(1,0),(0,1),(-1,0),(0,-1)]:
                    nr,nc = r+dr, c+dc
                    if 0<=nr<len(grid) and 0<=nc<len(grid[0]):
                        if grid[nr][nc] == 1:
                            return res
                        if grid[nr][nc] == 0:
                            island1.append((nr,nc))
                            grid[nr][nc] = -1
            res += 1
        return -1


        
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