<p>Given a 2D character matrix <code>grid</code>, where <code>grid[i][j]</code> is either <code>&#39;X&#39;</code>, <code>&#39;Y&#39;</code>, or <code>&#39;.&#39;</code>, return the number of <span data-keyword="submatrix">submatrices</span> that contain:</p>

<ul>
	<li><code>grid[0][0]</code></li>
	<li>an <strong>equal</strong> frequency of <code>&#39;X&#39;</code> and <code>&#39;Y&#39;</code>.</li>
	<li><strong>at least</strong> one <code>&#39;X&#39;</code>.</li>
</ul>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">grid = [[&quot;X&quot;,&quot;Y&quot;,&quot;.&quot;],[&quot;Y&quot;,&quot;.&quot;,&quot;.&quot;]]</span></p>

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

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

<p><strong><img alt="" src="https://assets.leetcode.com/uploads/2024/06/07/examplems.png" style="padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem; width: 175px; height: 350px;" /></strong></p>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">grid = [[&quot;X&quot;,&quot;X&quot;],[&quot;X&quot;,&quot;Y&quot;]]</span></p>

<p><strong>Output:</strong> <span class="example-io">0</span></p>

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

<p>No submatrix has an equal frequency of <code>&#39;X&#39;</code> and <code>&#39;Y&#39;</code>.</p>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">grid = [[&quot;.&quot;,&quot;.&quot;],[&quot;.&quot;,&quot;.&quot;]]</span></p>

<p><strong>Output:</strong> <span class="example-io">0</span></p>

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

<p>No submatrix has at least one <code>&#39;X&#39;</code>.</p>
</div>

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

<ul>
	<li><code>1 &lt;= grid.length, grid[i].length &lt;= 1000</code></li>
	<li><code>grid[i][j]</code> is either <code>&#39;X&#39;</code>, <code>&#39;Y&#39;</code>, or <code>&#39;.&#39;</code>.</li>
</ul>

class Solution:
    def numberOfSubmatrices(self, grid: List[List[str]]) -> int:
        xmark = False
        res = 0
        for i,row in enumerate(grid):
            if i == 0:
                for j,c in enumerate(row):
                    if j == 0:
                        if c == "X":
                            grid[0][0] = [1,0]
                        elif c == "Y":
                            grid[0][0] = [0,1]
                        else:
                            grid[0][0] = [0,0]
                    else: #top row but not 0,0
                        if c == "X":
                            grid[i][j] = [grid[i][j-1][0] + 1,grid[i][j-1][1]]
                        elif c == "Y":
                            grid[i][j] = [grid[i][j-1][0],grid[i][j-1][1] + 1]
                        else:
                            grid[i][j] = [grid[i][j-1][0],grid[i][j-1][1]]
                    if grid[i][j][0] >= 1 and grid[i][j][0] == grid[i][j][1]:
                        res += 1
            else:
                for j,c in enumerate(row):
                    if j == 0: #not top row but left column
                        if c == "X":
                            grid[i][j] = [grid[i-1][j][0] + 1,grid[i-1][j][1]]
                        elif c == "Y":
                            grid[i][j] = [grid[i-1][j][0],1+grid[i-1][j][1]]
                        else:
                            grid[i][j] = [grid[i-1][j][0],grid[i-1][j][1]]
                    else: #not top row and not left column
                        if c == "X":
                            grid[i][j] = [grid[i][j-1][0] + grid[i-1][j][0] - grid[i-1][j-1][0] + 1,grid[i][j-1][1] + grid[i-1][j][1] - grid[i-1][j-1][1]]
                        elif c == "Y":
                            grid[i][j] = [grid[i][j-1][0] + grid[i-1][j][0] - grid[i-1][j-1][0],grid[i][j-1][1] + grid[i-1][j][1] - grid[i-1][j-1][1] + 1]
                        else:
                            grid[i][j] = [grid[i][j-1][0] + grid[i-1][j][0] - grid[i-1][j-1][0],grid[i][j-1][1] + grid[i-1][j][1] - grid[i-1][j-1][1]]
                    if grid[i][j][0] >= 1 and grid[i][j][0] == grid[i][j][1]:
                        res += 1
        return res

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