<p>Given a string <code>expression</code> representing an expression of fraction addition and subtraction, return the calculation result in string format.</p>

<p>The final result should be an <a href="https://en.wikipedia.org/wiki/Irreducible_fraction" target="_blank">irreducible fraction</a>. If your final result is an integer, change it to the format of a fraction that has a denominator <code>1</code>. So in this case, <code>2</code> should be converted to <code>2/1</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> expression = &quot;-1/2+1/2&quot;
<strong>Output:</strong> &quot;0/1&quot;
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> expression = &quot;-1/2+1/2+1/3&quot;
<strong>Output:</strong> &quot;1/3&quot;
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> expression = &quot;1/3-1/2&quot;
<strong>Output:</strong> &quot;-1/6&quot;
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li>The input string only contains <code>&#39;0&#39;</code> to <code>&#39;9&#39;</code>, <code>&#39;/&#39;</code>, <code>&#39;+&#39;</code> and <code>&#39;-&#39;</code>. So does the output.</li>
	<li>Each fraction (input and output) has the format <code>&plusmn;numerator/denominator</code>. If the first input fraction or the output is positive, then <code>&#39;+&#39;</code> will be omitted.</li>
	<li>The input only contains valid <strong>irreducible fractions</strong>, where the <strong>numerator</strong> and <strong>denominator</strong> of each fraction will always be in the range <code>[1, 10]</code>. If the denominator is <code>1</code>, it means this fraction is actually an integer in a fraction format defined above.</li>
	<li>The number of given fractions will be in the range <code>[1, 10]</code>.</li>
	<li>The numerator and denominator of the <strong>final result</strong> are guaranteed to be valid and in the range of <strong>32-bit</strong> int.</li>
</ul>

class Solution:
    def fractionAddition(self, expression: str) -> str:
        num = []
        den = []
        i = 0
        sign = 1
        if expression[0]=='-':
            sign=-1
            i = 1
        cur = i
        while i<len(expression):
            if expression[i]=='/':
                num.append(sign*int(expression[cur:i]))
                cur = i+1
            if expression[i]=='+':
                den.append(int(expression[cur:i]))
                cur=i+1
                sign=1
            if expression[i]=='-':
                den.append(int(expression[cur:i]))
                cur=i+1
                sign=-1
            i+=1
        den.append(int(expression[cur:]))
        
        left = [1]*len(num)
        right = [1]*len(num)
        for i in range(1,len(num)):
            left[i] = left[i-1]*den[i-1]
            right[len(num)-1-i] = right[len(num)-i]*den[len(num)-i]
        
        d = left[-1]*den[-1]
        n = sum(num[i]*left[i]*right[i] for i in range(len(num)))

        f = gcd(d,n)
        d = d//f
        n = n//f
        return str(n) + '/' + str(d)
        
                    
16200