A Prüfer code of a tree of $n$ nodes is a sequence of $n-2$ integers that uniquely specifies the structure of the tree.
The code is constructed as follows: As long as there are at least three nodes left, find a leaf with the smallest label, add the label of its only neighbor to the code, and remove the leaf from the tree.
Given a Prüfer code of a tree, your task is to construct the original tree.
The first input line contains an integer $n$ : the number of nodes. The nodes are numbered $1,2,\ldots,n$ .
The second line contains $n-2$ integers: the Prüfer code.
Print $n-1$ lines describing the edges of the tree. Each line has to contain two integers $a$ and $b$ : there is an edge between nodes $a$ and $b$ . You can print the edges in any order.
5 2 2 4\n · · \n
1 2 2 3 2 4 4 5· \n · \n · \n · \n