<p>You are given a binary string <code>s</code>.</p>

<p>Return the number of <span data-keyword="substring-nonempty">substrings</span> with <strong>dominant</strong> ones.</p>

<p>A string has <strong>dominant</strong> ones if the number of ones in the string is <strong>greater than or equal to</strong> the <strong>square</strong> of the number of zeros in the string.</p>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">s = &quot;00011&quot;</span></p>

<p><strong>Output:</strong> <span class="example-io">5</span></p>

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

<p>The substrings with dominant ones are shown in the table below.</p>
</div>

<table>
	<thead>
		<tr>
			<th>i</th>
			<th>j</th>
			<th>s[i..j]</th>
			<th>Number of Zeros</th>
			<th>Number of Ones</th>
		</tr>
	</thead>
	<tbody>
		<tr>
			<td>3</td>
			<td>3</td>
			<td>1</td>
			<td>0</td>
			<td>1</td>
		</tr>
		<tr>
			<td>4</td>
			<td>4</td>
			<td>1</td>
			<td>0</td>
			<td>1</td>
		</tr>
		<tr>
			<td>2</td>
			<td>3</td>
			<td>01</td>
			<td>1</td>
			<td>1</td>
		</tr>
		<tr>
			<td>3</td>
			<td>4</td>
			<td>11</td>
			<td>0</td>
			<td>2</td>
		</tr>
		<tr>
			<td>2</td>
			<td>4</td>
			<td>011</td>
			<td>1</td>
			<td>2</td>
		</tr>
	</tbody>
</table>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">s = &quot;101101&quot;</span></p>

<p><strong>Output:</strong> <span class="example-io">16</span></p>

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

<p>The substrings with <strong>non-dominant</strong> ones are shown in the table below.</p>

<p>Since there are 21 substrings total and 5 of them have non-dominant ones, it follows that there are 16 substrings with dominant ones.</p>
</div>

<table>
	<thead>
		<tr>
			<th>i</th>
			<th>j</th>
			<th>s[i..j]</th>
			<th>Number of Zeros</th>
			<th>Number of Ones</th>
		</tr>
	</thead>
	<tbody>
		<tr>
			<td>1</td>
			<td>1</td>
			<td>0</td>
			<td>1</td>
			<td>0</td>
		</tr>
		<tr>
			<td>4</td>
			<td>4</td>
			<td>0</td>
			<td>1</td>
			<td>0</td>
		</tr>
		<tr>
			<td>1</td>
			<td>4</td>
			<td>0110</td>
			<td>2</td>
			<td>2</td>
		</tr>
		<tr>
			<td>0</td>
			<td>4</td>
			<td>10110</td>
			<td>2</td>
			<td>3</td>
		</tr>
		<tr>
			<td>1</td>
			<td>5</td>
			<td>01101</td>
			<td>2</td>
			<td>3</td>
		</tr>
	</tbody>
</table>

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

<ul>
	<li><code>1 &lt;= s.length &lt;= 4 * 10<sup>4</sup></code></li>
	<li><code>s</code> consists only of characters <code>&#39;0&#39;</code> and <code>&#39;1&#39;</code>.</li>
</ul>

class Solution:
    def numberOfSubstrings(self, s: str) -> int:
        
        n = len(s)
        cnt = 0

        zro = []
        for i in range(n):
            if s[i] == '0':
                zro.append(i)
        
        if len(zro) == 0:
            return int(n*(n+1)/2)

        zro_idx = 0
        for l in range(0, n):
            if zro_idx < len(zro) and zro[zro_idx] < l:
                zro_idx += 1
            
            valid_zro = []
            for z in range(zro_idx, min(len(zro), zro_idx+201)):
                valid_zro.append(zro[z])
            valid_zro.append(n)

            zro_cnt = 0
            last = l

            for ind in valid_zro:
                min_one = zro_cnt * zro_cnt
                min_ind = max( l + min_one + zro_cnt -1, last)
                if min_ind < ind:
                    cnt += int((ind - min_ind))
                last = ind
                zro_cnt += 1
        
        return int(cnt)


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