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

*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