Prüfer Code

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