<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>

typedef pair<int,int> PII;
typedef tuple<int,int,int> TII;

class Solution {
public:
    int minSteps(int n) {
        PII temp = make_pair(INT_MAX, INT_MAX);
        vector<PII> (n+1, temp);

        queue<TII> proc;
        //A, clipboard A, operations

        proc.push(make_tuple(1,0,0));
        proc.push(make_tuple(1,1,1));

        int ans=INT_MAX;

        while (!proc.empty()){
            TII newNode = proc.front(); proc.pop();
            // cout << get<0>(newNode) << " " << get<1>(newNode) << " " <<get<2>(newNode) <<endl;  

            if (get<0>(newNode) == n && get<2>(newNode) < ans){
                ans = get<2>(newNode);
            }


            //paste
            TII tempNodeCopy = make_tuple(get<0>(newNode) + get<1>(newNode),get<1>(newNode), get<2>(newNode)+1);
            if (get<1>(newNode)!=0 && get<0>(newNode) + get<1>(newNode) <= n ){
                proc.push(tempNodeCopy);

                //copy
                tempNodeCopy = make_tuple(get<0>(tempNodeCopy),get<0>(tempNodeCopy), get<2>(tempNodeCopy)+1);
                proc.push(tempNodeCopy);

            }
            

            
            // //copy
            // tempNodeCopy = make_tuple(get<0>(tempNodeCopy),get<0>(tempNodeCopy), get<2>(tempNodeCopy)+1);
            // proc.push(tempNodeCopy);
        }


        return ans;
        
    }
};
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