<p>Given a string <code>s</code> representing a valid expression, implement a basic calculator to evaluate it, and return <em>the result of the evaluation</em>.</p>

<p><strong>Note:</strong> You are <strong>not</strong> allowed to use any built-in function which evaluates strings as mathematical expressions, such as <code>eval()</code>.</p>

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

<pre>
<strong>Input:</strong> s = &quot;1 + 1&quot;
<strong>Output:</strong> 2
</pre>

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

<pre>
<strong>Input:</strong> s = &quot; 2-1 + 2 &quot;
<strong>Output:</strong> 3
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;(1+(4+5+2)-3)+(6+8)&quot;
<strong>Output:</strong> 23
</pre>

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

<ul>
	<li><code>1 &lt;= s.length &lt;= 3 * 10<sup>5</sup></code></li>
	<li><code>s</code> consists of digits, <code>&#39;+&#39;</code>, <code>&#39;-&#39;</code>, <code>&#39;(&#39;</code>, <code>&#39;)&#39;</code>, and <code>&#39; &#39;</code>.</li>
	<li><code>s</code> represents a valid expression.</li>
	<li><code>&#39;+&#39;</code> is <strong>not</strong> used as a unary operation (i.e., <code>&quot;+1&quot;</code> and <code>&quot;+(2 + 3)&quot;</code> is invalid).</li>
	<li><code>&#39;-&#39;</code> could be used as a unary operation (i.e., <code>&quot;-1&quot;</code> and <code>&quot;-(2 + 3)&quot;</code> is valid).</li>
	<li>There will be no two consecutive operators in the input.</li>
	<li>Every number and running calculation will fit in a signed 32-bit integer.</li>
</ul>

class Solution:
    def calculate(self, s: str) -> int:
        
        # O(n) stack
        stack = []

        # store the current number
        num = 0

        # store the sign value to multiply the number by 
        sign = 1
        output = 0

        # we want to remove all whitespaces
        elems = [char for char in s if char != " "]
        elems.append("+")


        for elem in elems:

            # process if the current elem is a digit
            if elem.isdigit():
                # multiply the current num by 10 and add this num
                # for consecutive digits
                num = num * 10 + int(elem)

            # process signs
            if elem in "+-":
                # move our current num to the output
                output += num*sign
                # set our sign to negative if this sign is negative
                sign = -1 if elem == "-" else 1
                # reset our number to 0
                num = 0
            
            # use num, res, and sign to calculate sum of numbers within the parentheses
            elif elem == "(":
                # move output and sign to stack
                stack.append(output)
                stack.append(sign)
                # reset output and sign
                output = 0
                sign = 1


            elif elem == ")":
                # calculate sum for num first
                output += sign * num
                # then pop items from stack
                # pop the sign to multiply with the output
                output *=stack.pop()
                # pop the integer to add to the rest of the output
                output +=stack.pop()

                # reset our number to 0
                num = 0
        
        return output
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