<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):
        s.replace(' ', '')
        operators = set(['+', '-'])
        braces = set(['(', ')'])
        stack = []
        inbraces = False
        if s[0] == '-':
            s= '0' + s
        for i in range(len(s)):
            if s[i] in operators or s[i] in braces or (s[i].lstrip("-").isdigit() and len(stack) == 0):
                stack.append(s[i])
            elif s[i].lstrip("-").isdigit():
                if (stack[-1] in operators and (len(stack) == 1 or( len(stack)>1 and stack[-2] =='('))):
                    stack.append(stack.pop() + s[i])
                elif stack[-1].lstrip("-").isdigit():
                    stack.append(stack.pop() + s[i])
                else:
                    stack.append(s[i])
        # print(stack)
        open_par = []
        end = 0
        i= 0
        while i < len(stack):
            if stack[i] == '(':
                open_par.append(i)
            elif stack[i] == ')':
                end = i
                start = open_par.pop()
                sub_exp = stack[start+1:end]
                evaluated_exp = Solution.calc(sub_exp)
                # print(f'sub_exp {sub_exp}')
                new_exp = stack[:start] + [evaluated_exp] + stack[end+1:]
                stack = new_exp
                i = start - 1
            i +=1
        
        return int(Solution.calc(stack))

    def calc(stack):
        # print(f'calc stack{stack}')
        if len(stack) == 1:
            return stack[0]
        elif len(stack) == 2:
            return stack[0] + stack[1]
        elif len(stack) > 2 and stack[0].lstrip("-").isdigit() and stack[2].lstrip("-").isdigit():
            val1 = stack.pop(0)
            operator = stack.pop(0)
            val2 = stack.pop(0)
            if operator == '+':
                stack.insert(0, str(int(val1) + int(val2)))
            else:
                stack.insert(0, str(int(val1) - int(val2)))
            return Solution.calc(stack)
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