**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