<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:
        # step 1: tokenize
        tokens = []
        i = 0
        while i < len(s):
            if s[i] == '(':
                tokens.append({
                    'token_type': 'LPAREN',
                    'lexeme': '('
                })
                i += 1
            elif s[i] == ')':
                tokens.append({
                    'token_type': 'RPAREN',
                    'lexeme': ')'
                })
                i += 1
            elif s[i] in '+-':
                tokens.append({
                    'token_type': 'OP',
                    'lexeme': s[i]
                })
                i += 1
            elif s[i].isdigit():
                number = ''
                while i < len(s) and s[i].isdigit():
                    number += s[i]
                    i += 1
                tokens.append({
                    'token_type': 'NUM',
                    'lexeme': int(number)
                })
            else: # space
                i += 1

        # step 2: parse
        pos = 0
        def parseAtom():
            nonlocal pos
            if tokens[pos]['token_type'] == 'OP' and tokens[pos]['lexeme'] == '-':
                pos += 1
                return -parseAtom()
            elif tokens[pos]['token_type'] == 'NUM':
                val = tokens[pos]['lexeme']
                pos += 1
                return val
            elif tokens[pos]['lexeme'] == '(':
                pos += 1
                res = parseExpr()
                pos += 1
                return res
        
        def parseExpr():
            nonlocal pos
            res = parseAtom()
            while pos < len(tokens) and tokens[pos]['token_type'] == 'OP':
                operator = tokens[pos]['lexeme']
                pos += 1
                if operator == '+':
                    res += parseAtom()
                else:
                    res -= parseAtom()
            return res
        return parseExpr()
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