<p>There is only one character <code>&#39;A&#39;</code> on the screen of a notepad. You can perform one of two operations on this notepad for each step:</p>

<ul>
	<li>Copy All: You can copy all the characters present on the screen (a partial copy is not allowed).</li>
	<li>Paste: You can paste the characters which are copied last time.</li>
</ul>

<p>Given an integer <code>n</code>, return <em>the minimum number of operations to get the character</em> <code>&#39;A&#39;</code> <em>exactly</em> <code>n</code> <em>times on the screen</em>.</p>

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

<pre>
<strong>Input:</strong> n = 3
<strong>Output:</strong> 3
<strong>Explanation:</strong> Initially, we have one character &#39;A&#39;.
In step 1, we use Copy All operation.
In step 2, we use Paste operation to get &#39;AA&#39;.
In step 3, we use Paste operation to get &#39;AAA&#39;.
</pre>

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

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> 0
</pre>

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

<ul>
	<li><code>1 &lt;= n &lt;= 1000</code></li>
</ul>

class Solution:
    def minSteps(self, n: int) -> int:
        if n == 1:
            return 0
        self.dic = {}

        def calc(cur_st , copy_st , steps , n , copy_status):
            if len(cur_st) == n:
                return steps

            if len(cur_st) > n:
                return float("inf")

            if cur_st in self.dic and copy_st in self.dic[cur_st]:
                return self.dic[cur_st][copy_st]

            #copy
            copy_steps = float('inf')

            if copy_status == False:
                copy_steps = calc(cur_st , cur_st , steps + 1 , n , True)
                
            #paste
            paste_steps = calc(cur_st + copy_st , copy_st , steps + 1 , n , False)

            if cur_st not in self.dic:
                self.dic[cur_st] = {}

            self.dic[cur_st][copy_st] = min(copy_steps , paste_steps)
            return min(copy_steps , paste_steps)
        
        return calc('A' , 'A' , 1 , n , True)
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