<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:
        s = s.replace(" ","")
        def calc(i,j):
            if i == j: return 0
            if j-i < 400:
                return eval(s[i:j])
            if s[i] == "(":
                balance = 1
                k = i+1
                while balance > 0:
                    if s[k] == "(":
                        balance += 1
                    if s[k] == ")":
                        balance -= 1
                    k += 1
                return calc(i+1,k-1)+calc(k,j)
            elif s[i] == "-":
                if s[i+1].isdigit():
                    k = i+1
                    while k < j and s[k].isdigit():
                        k += 1
                    return -int(s[i+1:k])+calc(k,j)
                else:
                    balance = 1
                    k = i+2
                    while balance > 0:
                        if s[k] == "(":
                            balance += 1
                        if s[k] == ")":
                            balance -= 1
                        k += 1
                    return -calc(i+2,k-1)+calc(k,j)
            elif s[i] == "+":
                return calc(i+1,j)
            else:
                k = i
                while k < j and s[k].isdigit():
                    k += 1
                return int(s[i:k])+calc(k,j)
        return calc(0,len(s))
                

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