<p>You are given a <strong>0-indexed</strong> string <code>expression</code> of the form <code>&quot;&lt;num1&gt;+&lt;num2&gt;&quot;</code> where <code>&lt;num1&gt;</code> and <code>&lt;num2&gt;</code> represent positive integers.</p>

<p>Add a pair of parentheses to <code>expression</code> such that after the addition of parentheses, <code>expression</code> is a <strong>valid</strong> mathematical expression and evaluates to the <strong>smallest</strong> possible value. The left parenthesis <strong>must</strong> be added to the left of <code>&#39;+&#39;</code> and the right parenthesis <strong>must</strong> be added to the right of <code>&#39;+&#39;</code>.</p>

<p>Return <code>expression</code><em> after adding a pair of parentheses such that </em><code>expression</code><em> evaluates to the <strong>smallest</strong> possible value.</em> If there are multiple answers that yield the same result, return any of them.</p>

<p>The input has been generated such that the original value of <code>expression</code>, and the value of <code>expression</code> after adding any pair of parentheses that meets the requirements fits within a signed 32-bit integer.</p>

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

<pre>
<strong>Input:</strong> expression = &quot;247+38&quot;
<strong>Output:</strong> &quot;2(47+38)&quot;
<strong>Explanation:</strong> The <code>expression</code> evaluates to 2 * (47 + 38) = 2 * 85 = 170.
Note that &quot;2(4)7+38&quot; is invalid because the right parenthesis must be to the right of the <code>&#39;+&#39;</code>.
It can be shown that 170 is the smallest possible value.
</pre>

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

<pre>
<strong>Input:</strong> expression = &quot;12+34&quot;
<strong>Output:</strong> &quot;1(2+3)4&quot;
<strong>Explanation:</strong> The expression evaluates to 1 * (2 + 3) * 4 = 1 * 5 * 4 = 20.
</pre>

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

<pre>
<strong>Input:</strong> expression = &quot;999+999&quot;
<strong>Output:</strong> &quot;(999+999)&quot;
<strong>Explanation:</strong> The <code>expression</code> evaluates to 999 + 999 = 1998.
</pre>

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

<ul>
	<li><code>3 &lt;= expression.length &lt;= 10</code></li>
	<li><code>expression</code> consists of digits from <code>&#39;1&#39;</code> to <code>&#39;9&#39;</code> and <code>&#39;+&#39;</code>.</li>
	<li><code>expression</code> starts and ends with digits.</li>
	<li><code>expression</code> contains exactly one <code>&#39;+&#39;</code>.</li>
	<li>The original value of <code>expression</code>, and the value of <code>expression</code> after adding any pair of parentheses that meets the requirements fits within a signed 32-bit integer.</li>
</ul>

class Solution:
    def minimizeResult(self, expression: str) -> str:
        min_ans = float('inf')
        min_str = ""
        
        # find the pos of "+"
        for idx in range(len(expression)):
            if expression[idx] == "+":
                break
        # print("idx", idx)
        
        for i in range(0, idx, 1):
            # calc left part
            left_part = 1
            if len(expression[:i]) > 0:
                left_part = int(expression[:i])
            for j in range(idx+2, len(expression)+1, 1):
                # print("formed expression", expression[:i] + "(" + expression[i:j] + ")" + expression[j:])
                # calc right part
                right_part = 1
                if len(expression[j:]) > 0:
                    right_part = int(expression[j:])
                # calc middle part
                if len(expression[i:idx])==0 and len(expression[idx+1:j])==0:
                    middle_part = 1
                elif len(expression[i:idx])==0:
                    middle_part = int(expression[idx+1:j])
                elif len(expression[idx+1:j])==0:
                    middle_part = int(expression[i:idx])
                else:
                    middle_part = int(expression[i:idx]) + int(expression[idx+1:j])

                if left_part * middle_part * right_part <= min_ans:
                    # print("updating")
                    min_ans = left_part * middle_part * right_part
                    min_str = expression[:i] + "(" + expression[i:j] + ")" + expression[j:]
                    # print(min_ans, min_str)
        return min_str  
                




        
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