<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:
        res = [[0] * len(grid[0]) for _ in range(len(grid))]
        res1 = [[0] * len(grid[0]) for _ in range(len(grid))]
        for i in range(len(grid[0])):
            if i == 0:
                if grid[0][i] == "X":
                    res[0][i] += 1
                    res1[0][i] += 1
                elif grid[0][i] == "Y":
                    res[0][i] -= 1
            else:
                if grid[0][i] == "X":
                    res[0][i] = res[0][i-1] + 1
                    res1[0][i] = res1[0][i-1] + 1
                elif grid[0][i] == "Y":
                    res[0][i] = res[0][i-1] - 1
                    res1[0][i] = res1[0][i-1]
                else:
                    res1[0][i] = res1[0][i-1]
                    res[0][i] = res[0][i-1]
        for i in range(len(grid)):
            if i == 0:
                if grid[i][0] == "X":
                    res[i][0] = 1
                    res1[i][0] = 1
                elif grid[i][0] == "Y":
                    res[i][0] = -1
            else:
                if grid[i][0] == "X":
                    res[i][0] = res[i-1][0] + 1
                    res1[i][0] = res1[i-1][0] + 1
                elif grid[i][0] == "Y":
                    res[i][0] = res[i-1][0] - 1
                    res1[i][0] = res1[i-1][0]
                else:
                    res1[i][0] = res1[i-1][0]
                    res[i][0] = res[i-1][0]
        for i in range(1, len(grid)):
            for j in range(1, len(grid[0])):
                res[i][j] = res[i-1][j] + res[i][j-1] - res[i-1][j-1]
                if grid[i][j] == "X":
                    res[i][j] += 1
                    res1[i][j] = 1
                elif grid[i][j] == "Y":
                    res[i][j] -= 1
                    res1[i][j] = 1 if res1[i][j-1] > 0 or res1[i-1][j] > 0 else 0
                else:
                    res1[i][j] = 1 if res1[i][j-1] > 0 or res1[i-1][j] > 0 else 0
        count = 0
        for i in range(len(grid)):
            for j in range(len(grid[0])):
                if res1[i][j] > 0 and res[i][j] == 0:
                    count += 1
        return count
61851