<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 Expr:
    def __init__(self):
        self.tokens = []
        self.ops = []

    def ingest(self, iter):
        for t in iter:
            match t:
                case '+':
                    self.ops.append(lambda x, y: x + y)
                case '-':
                    self.ops.append(lambda x, y: x - y)
                case '(':
                    nestedExpr = Expr()
                    nestedExpr.ingest(iter)
                    self.tokens.append(nestedExpr)
                case ')':
                    return
                case _:
                    self.tokens.append(t)
        return self

    def valueOf(self, token):
        if isinstance(token, Expr):
            return token.eval()
        return token

    def eval(self):
        curr = self.valueOf(self.tokens[0])
        for i in range(len(self.ops)):
            curr = self.ops[i](curr, self.valueOf(self.tokens[i + 1]))
        return curr

class Solution:
    def tokenize(self, s: str) -> list[str]: 
        numAcc = ''
        tokens = []
        expectingExpression = True
        for c in s:
            match c:
                case '+':
                    if numAcc:
                        n = int(numAcc)
                        tokens.append(n)
                        numAcc = ''
                    tokens.append(c)
                    expectingExpression = True
                case '-':
                    if numAcc:
                        n = int(numAcc)
                        tokens.append(n)
                        tokens.append(c)
                        numAcc = ''    
                        expectingExpression = True
                    elif expectingExpression:
                        tokens.append(0)
                        tokens.append(c)
                    else:
                        tokens.append(c)
                        
                case '(':
                    if numAcc:
                        n = int(numAcc)
                        tokens.append(n)
                        numAcc = ''
                    tokens.append(c)
                    expectingExpression = True
                case ')':
                    if numAcc:
                        n = int(numAcc)
                        tokens.append(n)
                        numAcc = ''
                    tokens.append(c)
                    expectingExpression = False
                case ' ':
                    if numAcc:
                        n = int(numAcc)
                        tokens.append(n)
                        numAcc = ''
                        expectingExpression = False
                case _:
                    numAcc += c
        if numAcc:
            tokens.append(int(numAcc))
        
        return tokens


    def calculate(self, s: str) -> int:
        tokens = self.tokenize(s)
        return Expr().ingest((t for t in tokens)).eval()
        
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