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CSES Problem Set

Prüfer Code

CSES - Prüfer CodeCSES - Prüfer Code

 Time limit: 1.00 s Memory limit: 512 MB

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.

Input

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.

Output

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.

Constraints
• $3 \le n \le 2 \cdot 10^5$
• $1 \le a,b \le n$
Example

Input:
5
2 2 4

Output:
1 2
2 3
2 4
4 5