<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:
        def recursive(self, n):
            #recursive with backtracking
            # store current action count, clipboard, and notepad

            def recursiveHelper(notepad, clipboard, count, target, ans):
                if len(notepad) == target: # we have answer once we reach count
                    ans.add(count)
                    return
                elif len(notepad) > target: # if the length exceeds the target, then do nothing
                    return

                # one of two actions
                # copy clipboard
                if notepad != clipboard:
                    recursiveHelper(notepad, notepad, count+1, target, ans)
                # paste onto notepad
                if clipboard != "":
                    recursiveHelper(notepad+clipboard, clipboard, count+1, target, ans)
 
            ans = set()
            recursiveHelper('A', '', 0, n, ans)
            return min(ans)
 
        def bfs(self, n): # memory limit exceeded
            # can use a deque for a FIFO queue
            # for each item, simulate either copying or pasting clipboard
            # if number of characters ever reach N characters, we return the number of actions

            dq = deque()
            dq.append(('A',"",0)) # current notepad, clipboard, number of events

            # BFS for all possible states
            while True:
                sz = len(dq)
                for i in range(sz):
                    t = dq.popleft()
                    # if we have reached the number of characters, return with number of events
                    if len(t[0]) == n:
                        return t[2]
                    # if actions exceed the limit, then don't do them
                    elif len(t[0]) > n:
                        continue

                    # possible two actions
                    # 1 - copy clipboard
                    if t[0] != t[1]:
                        dq.append((t[0], t[0], t[2]+1))
                    # 2 - paste clipboard if possile
                    if t[1] != "":
                        dq.append((t[0]+t[1], t[1], t[2]+1))
        
        return bfs(self, n)
29468