<p>Given an integer <code>n</code>, find a sequence that satisfies all of the following:</p>

<ul>
	<li>The integer <code>1</code> occurs once in the sequence.</li>
	<li>Each integer between <code>2</code> and <code>n</code> occurs twice in the sequence.</li>
	<li>For every integer <code>i</code> between <code>2</code> and <code>n</code>, the <strong>distance</strong> between the two occurrences of <code>i</code> is exactly <code>i</code>.</li>
</ul>

<p>The <strong>distance</strong> between two numbers on the sequence, <code>a[i]</code> and <code>a[j]</code>, is the absolute difference of their indices, <code>|j - i|</code>.</p>

<p>Return <em>the <strong>lexicographically largest</strong> sequence</em><em>. It is guaranteed that under the given constraints, there is always a solution. </em></p>

<p>A sequence <code>a</code> is lexicographically larger than a sequence <code>b</code> (of the same length) if in the first position where <code>a</code> and <code>b</code> differ, sequence <code>a</code> has a number greater than the corresponding number in <code>b</code>. For example, <code>[0,1,9,0]</code> is lexicographically larger than <code>[0,1,5,6]</code> because the first position they differ is at the third number, and <code>9</code> is greater than <code>5</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 3
<strong>Output:</strong> [3,1,2,3,2]
<strong>Explanation:</strong> [2,3,2,1,3] is also a valid sequence, but [3,1,2,3,2] is the lexicographically largest valid sequence.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 5
<strong>Output:</strong> [5,3,1,4,3,5,2,4,2]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 20</code></li>
</ul>

class Solution {
public:
    set<vector<int>> st;
    bool solve(int n,int index,vector<int>&arr,vector<int>&visited)
    {
        if(index >= arr.size())
        {
            
            return true;
        }
        if(arr[index] != -1)
        {
            return solve(n,index+1,arr,visited);
        
        }
         
        for(int i=n;i>=1;i--)
        {
            
            if(!visited[i])
            {
                 if(i == 1)
                 {
                      arr[index]=i;
                      visited[i]=1;
                    if(solve(n,index+1,arr,visited))return true;
                      arr[index]=-1;
                      visited[i]=0;
                 }
               else if(index+i < arr.size() and arr[index+i] == -1)
                 {
                      arr[index]=i;  
                      arr[index+i]=i;
                      visited[i]=1;
                      if(solve(n,index+1,arr,visited))return true;
                      arr[index]=-1;
                      arr[index+i]=-1;
                      visited[i]=0;
                 }
            }
        }
        return false;
        
    }
    vector<int> constructDistancedSequence(int n) {
        vector<int> arr(2*n-1,-1);
        vector<int> visited(n+1,false);
        solve(n,0,arr,visited);
       
        return arr;
    }
};
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