<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:
        self.dp = set()
        def backtracking(n_A, n_A_in_copy, copied_last_time):
            if n_A > n:
                return -1
            if n_A == n:
                return 0
            if (n_A, n_A_in_copy) in self.dp:
                return -1
            ans_copy, ans_paste = -1, -1
            if not copied_last_time:
                # Copy
                ans_copy = backtracking(n_A, n_A, True)
            if n_A_in_copy > 0:
                # Paste
                ans_paste = backtracking(n_A + n_A_in_copy, n_A_in_copy, False)
            if ans_copy == -1 and ans_paste == -1:
                self.dp.add((n_A, n_A_in_copy))
                return -1
            # print(n_A, n_A_in_copy, copied_last_time, ans_copy, ans_paste)
            if ans_copy == -1:
                return ans_paste + 1
            elif ans_paste == -1:
                return ans_copy + 1
            else:
                return min(ans_copy, ans_paste) + 1

        return backtracking(1, 0, False)
            
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