<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:
        d=dict()
        arr=[0]*len(s)
        Sum=0
        Sign=0
        for i in range(len(s)):
            if Sign==0 and s[i]=='1':
                k=i
                d[i]=i
                Sign=1
            elif Sign==1 and s[i]=='0':
                d[k]=i-1
                Sign=0
            elif Sign==1:
                d[k]=i
            if s[i]=='1':
                Sum=Sum+1
            arr[i]=Sum
        Sum,i,j,f=0,0,0,0
        while i<len(s):
            if i in d:
                Sum=Sum+((d[i]-i+1)*(d[i]-i+2))//2
                f=d[i]+1
            if i<f:
                j=f
            else:
                j=i
            while j<len(s):
                ones=arr[j]-arr[i]+int(s[i])
                zeros=(j-i+1)-ones
                if ones>zeros**2:
                    diff=int(math.sqrt(ones))-zeros
                    if j+diff>len(s):
                        Sum=Sum+len(s)-j
                        j=len(s)
                    elif diff==0:
                        Sum=Sum+1
                        j=j+1
                    else:
                        Sum=Sum+diff
                        j=j+diff
                elif ones==zeros**2:
                    Sum=Sum+1
                    j=j+1
                else:
                    diff=zeros**2-ones
                    j=j+diff
            i=i+1 
        return Sum 
19800