<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 {
public:
    int recur(map<vector<int>, int>& m, int copy, int cur, int n, int op, int prev){
        if(cur > n)
            return INT_MAX;
        if(cur == n){
            if(m.count({copy, cur, prev}))
                return m[{copy, cur, prev}] = min(m[{copy, cur, prev}], op);
            return m[{copy, cur, prev}] = op;
        }
        if(m.count({copy, cur, prev}))
            return m[{copy, cur, prev}];
        // Either paste which counts as one op
        // Copy and then paste because it doesnt make sense to copy twice. 2 ops

        return m[{copy, cur, prev}] = min(copy == 0 ? INT_MAX : recur(m, copy, cur + prev, n, op + 1, prev), recur(m, copy + 1, cur * 2, n, op + 2, cur));
    }
    int minSteps(int n) {
        // Three variables change. No. of times copy was used and what the current state was, and what is the copied state
        /*
        So if we have 'AAA' and it has copy operation once, we represent this state as 
        C = 1, cur = 3, prev = 1
        */
        map<vector<int>, int> m;
        return recur(m, 0, 1, n, 0, 0);
    }
};
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