<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 Token:
    def __init__(self, val, type, priority, op_type=None) -> None:
        self.val = val
        self.type = type
        self.priority = priority
        self.op_type = op_type

def is_number(c):
    numbers = {'1','2','3','4','5','6','7','8','9','0'}

    return c in numbers


def tokenizer(s):
    i = 0
    tokens = []

    while i < len(s):

        if s[i] == ' ':
            i += 1
            continue

        if is_number(s[i]):
            number = s[i]
            i += 1
            while i < len(s) and is_number(s[i]):
                number += s[i]
                i += 1
            tokens.append(Token(number, 'NUM', 10))
            continue

        elif s[i] == '+':
            tokens.append(Token(s[i], 'OPERATION', 50, 'BINARY'))
        elif s[i] == '-':
            if len(tokens) == 0 or (tokens[-1].type != 'NUM' and tokens[-1].type != 'BR'):
                tokens.append(Token(s[i], 'OPERATION', 100, 'UNARY'))
            else:
                tokens.append(Token(s[i], 'OPERATION', 50, 'BINARY'))
        elif s[i] == '*' or s[i] == '/':
            tokens.append(Token(s[i], 'OPERATION', 60, 'BINARY'))
        elif s[i] == '(':
            tokens.append(Token(s[i], 'BL', 15))
        elif s[i] == ')':
            tokens.append(Token(s[i], 'BR', 15))


        i += 1

    return tokens



def to_rpn(tokens):
    expr = []
    stack = []

    for tok in tokens:
        if tok.type == 'NUM':
            expr.append(tok)
        elif tok.type == 'OPERATION':
            if tok.op_type == 'UNARY':
                stack.append(tok)
            elif tok.op_type == 'BINARY':
                while len(stack) > 0 and stack[-1].priority >= tok.priority:
                    expr.append(stack.pop())
                stack.append(tok)
        elif tok.type == 'BL':
            stack.append(tok)
        elif tok.type == 'BR':
            while stack[-1].val != '(':
                expr.append(stack.pop())
            stack.pop()

    while len(stack) > 0:
        expr.append(stack.pop())

    return expr

def evaluate(expr):
    calc = []
    for val in expr:
        if val.type == 'NUM':
            calc.append(int(val.val))
        else:
            if val.val == '+':
                calc.append((calc.pop()) + (calc.pop()))
            elif val.val == '-' and val.op_type == 'BINARY':
                calc.append(-(calc.pop()) + (calc.pop()))
            elif val.val == '-' and val.op_type == 'UNARY':
                calc.append(-(calc.pop()))
            elif val.val == '*':
                calc.append((calc.pop()) * (calc.pop()))
            elif val.val == '/':
                calc.append(int(1 / (calc.pop()) * (calc.pop())))

    return calc[0]

class Solution:
    def calculate(self, s: str) -> int:
        return int(evaluate(to_rpn(tokenizer(s))))

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