<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 minSteps(int n) {
        // if(n == 1)
        //     return 0;
        // if(n == 2)
        //     return 2;
        // if(n % 2)
        //     return n;
        // else
        //     return n / 2 + 2;

        if(n == 1)
            return 0;
        queue<pair<int, pair<int, int>>> q;
        q.push({1, {1, 1}});
        pair<int, pair<int, int>> a;
        int ans = n;
        while(!q.empty()){
            a = q.front();
            q.pop();
            if(a.first == n){
                ans = min(ans, a.second.second);
            }
            if(a.first + a.second.first <= n){
                q.push({a.first + a.second.first, {a.second.first, a.second.second + 1}});
            }
            if(a.first + a.first <= n){
                q.push({a.first + a.first, {a.first, a.second.second + 2}});
            }
        }
        return ans;
    }
};
58696