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Algorithms

Given a string <code>s</code>, return whether <code>s</code> is a valid number. 
 
For example, all the following are valid numbers: <code>&quot;2&quot;, &quot;0089&quot;, &quot;-0.1&quot;, &quot;+3.14&quot;, &quot;4.&quot;, &quot;-.9&quot;, &quot;2e10&quot;, &quot;-90E3&quot;, &quot;3e+7&quot;, &quot;+6e-1&quot;, &quot;53.5e93&quot;, &quot;-123.456e789&quot;</code>, while the following are not valid numbers: <code>&quot;abc&quot;, &quot;1a&quot;, &quot;1e&quot;, &quot;e3&quot;, &quot;99e2.5&quot;, &quot;--6&quot;, &quot;-+3&quot;, &quot;95a54e53&quot;</code>.

Formally, a&nbsp;valid number is defined using one of the following definitions:

<ol>
	<li>An integer number followed by an optional exponent.</li>
	<li>A decimal number followed by an optional exponent.</li>
</ol>

An integer number is defined with an optional sign <code>&#39;-&#39;</code> or <code>&#39;+&#39;</code> followed by digits.

A decimal number is defined with an optional sign <code>&#39;-&#39;</code> or <code>&#39;+&#39;</code> followed by one of the following definitions:

<ol>
	<li>Digits followed by a dot <code>&#39;.&#39;</code>.</li>
	<li>Digits followed by a dot <code>&#39;.&#39;</code> followed by digits.</li>
	<li>A dot <code>&#39;.&#39;</code> followed by digits.</li>
</ol>

An exponent is defined with an exponent notation <code>&#39;e&#39;</code> or <code>&#39;E&#39;</code> followed by an integer number.

The digits are defined as one or more digits.

&nbsp;
Example 1:

<div class="example-block">
Input: s = &quot;0&quot;

Output: true
</div>

Example 2:

<div class="example-block">
Input: s = &quot;e&quot;

Output: false
</div>

Example 3:

<div class="example-block">
Input: s = &quot;.&quot;

Output: false
</div>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= s.length &lt;= 20</code></li>
	<li><code>s</code> consists of only English letters (both uppercase and lowercase), digits (<code>0-9</code>), plus <code>&#39;+&#39;</code>, minus <code>&#39;-&#39;</code>, or dot <code>&#39;.&#39;</code>.</li>
</ul>