<p>Given an <code>n x n</code> binary <code>grid</code>, in one step you can choose two <strong>adjacent rows</strong> of the grid and swap them.</p>

<p>A grid is said to be <strong>valid</strong> if all the cells above the main diagonal are <strong>zeros</strong>.</p>

<p>Return <em>the minimum number of steps</em> needed to make the grid valid, or <strong>-1</strong> if the grid cannot be valid.</p>

<p>The main diagonal of a grid is the diagonal that starts at cell <code>(1, 1)</code> and ends at cell <code>(n, n)</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/07/28/fw.jpg" style="width: 750px; height: 141px;" />
<pre>
<strong>Input:</strong> grid = [[0,0,1],[1,1,0],[1,0,0]]
<strong>Output:</strong> 3
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/07/16/e2.jpg" style="width: 270px; height: 270px;" />
<pre>
<strong>Input:</strong> grid = [[0,1,1,0],[0,1,1,0],[0,1,1,0],[0,1,1,0]]
<strong>Output:</strong> -1
<strong>Explanation:</strong> All rows are similar, swaps have no effect on the grid.
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/07/16/e3.jpg" style="width: 200px; height: 200px;" />
<pre>
<strong>Input:</strong> grid = [[1,0,0],[1,1,0],[1,1,1]]
<strong>Output:</strong> 0
</pre>

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

<ul>
	<li><code>n == grid.length</code> <code>== grid[i].length</code></li>
	<li><code>1 &lt;= n &lt;= 200</code></li>
	<li><code>grid[i][j]</code> is either <code>0</code> or <code>1</code></li>
</ul>

class Solution:
    def minSwaps(self, grid: List[List[int]]) -> int:
        max_rights = []
        n = len(grid)
        swaps = 0

        for i in range(n):
            count = 0
            for j in range(n-1, -1, -1):
                if grid[i][j] == 1:
                    break
                count += 1
            max_rights.append(count)
        
        for i in range(n):
            target = n - i - 1
            suitable = -1
            for j in range(i, n):
                if max_rights[j] >= target:
                    suitable = j
                    break

            if suitable == -1:
                return -1
            
            while suitable > i:
                max_rights[suitable], max_rights[suitable-1] = max_rights[suitable-1], max_rights[suitable]
                suitable -= 1
                swaps += 1

        return swaps
17600