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**Task** | Statistics

Time limit: | 1.00 s | Memory limit: | 512 MB |

A

The code is constructed as follows: As long as there are at least three nodes, find a leaf whose label is minimum, add the label of its only neighbor to the code, and remove the node 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 that describe 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.

- $3 \le n \le 5 \cdot 10^5$

- $1 \le a,b \le n$

Input:

`5`

2 2 4

Output:

`1 2`

2 3

2 4

4 5