<p>You are given a <code>m x n</code> 2D array <code>board</code> representing a chessboard, where <code>board[i][j]</code> represents the <strong>value</strong> of the cell <code>(i, j)</code>.</p>

<p>Rooks in the <strong>same</strong> row or column <strong>attack</strong> each other. You need to place <em>three</em> rooks on the chessboard such that the rooks <strong>do not</strong> <strong>attack</strong> each other.</p>

<p>Return the <strong>maximum</strong> sum of the cell <strong>values</strong> on which the rooks are placed.</p>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">board = </span>[[-3,1,1,1],[-3,1,-3,1],[-3,2,1,1]]</p>

<p><strong>Output:</strong> 4</p>

<p><strong>Explanation:</strong></p>

<p><img alt="" src="https://assets.leetcode.com/uploads/2024/08/08/rooks2.png" style="width: 294px; height: 450px;" /></p>

<p>We can place the rooks in the cells <code>(0, 2)</code>, <code>(1, 3)</code>, and <code>(2, 1)</code> for a sum of <code>1 + 1 + 2 = 4</code>.</p>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">board = [[1,2,3],[4,5,6],[7,8,9]]</span></p>

<p><strong>Output:</strong> <span class="example-io">15</span></p>

<p><strong>Explanation:</strong></p>

<p>We can place the rooks in the cells <code>(0, 0)</code>, <code>(1, 1)</code>, and <code>(2, 2)</code> for a sum of <code>1 + 5 + 9 = 15</code>.</p>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">board = [[1,1,1],[1,1,1],[1,1,1]]</span></p>

<p><strong>Output:</strong> <span class="example-io">3</span></p>

<p><strong>Explanation:</strong></p>

<p>We can place the rooks in the cells <code>(0, 2)</code>, <code>(1, 1)</code>, and <code>(2, 0)</code> for a sum of <code>1 + 1 + 1 = 3</code>.</p>
</div>

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

<ul>
	<li><code>3 &lt;= m == board.length &lt;= 100</code></li>
	<li><code>3 &lt;= n == board[i].length &lt;= 100</code></li>
	<li><code>-10<sup>9</sup> &lt;= board[i][j] &lt;= 10<sup>9</sup></code></li>
</ul>

from sortedcontainers import SortedList
class Solution:
    def maximumValueSum(self, board: List[List[int]]) -> int:
        def compute(board):
            m = len(board)
            n = len(board[0])
            row = []
            arr=[]
            for i in range(m):
                # arr = []
                for j in range(n):
                    arr.append([i,j,board[i][j]])
                # arr.sort(key = lambda x  :-x[-1])
                # row.append(arr[:3])
                
            arr.sort(key = lambda x : -x[2])
            # row = row[:3]
            res=float('-inf')
            # print(row)
            # for i in row:
            #     print(i)
            r = len(row)
            arr = arr[:60]
            for a,b,cost1 in arr:
                for c,d,cost2 in arr:
                    for e,f,cost3 in arr:
                        set1 = set([a,c,e])
                        set2 = set([b,d,f])
                        if len(set1)==3 and len(set2)==3:
                            res = max(board[a][b]+board[c][d]+board[e][f] , res)
                            
            # [[-95,-22,85,-57],
            #  [-4,10   ,80,68],
            #  [-20,-59,99,-97],
            #  [-25,-60,71,21]]
            return res
        # transpose = []
        # for x in zip(*board):
        #     transpose.append(list(x))
        # print(transpose)
        return compute(board)
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