youngmaids
Problem Statement
Let N be a positive even number.
We have a permutation of (1, 2, ..., N), p = (p1, p2, ..., pN).
Snuke is constructing another permutation of (1, 2, ..., N), q, following the procedure below.
First, let q be an empty sequence.
Then, perform the following operation until p becomes empty:
- Select two adjacent elements in p, and call them x and y in order. Remove x and y from p (reducing the length of p by 2), and insert x and y, preserving the original order, at the beginning of q.
When p becomes empty, q will be a permutation of (1, 2, ..., N).
Find the lexicographically smallest permutation that can be obtained as q.
Constraints
- N is an even number.
- 2 ≤ N ≤ 2 × 105
- p is a permutation of (1, 2, ..., N).
Input
Input is given from Standard Input in the following format:
N
p1 p2 ... pN
Output
Print the lexicographically smallest permutation, with spaces in between.
Sample Input 1
4
3 2 4 1
Sample Output 1
3 1 2 4
The solution above is obtained as follows:
| p |
q |
| (3, 2, 4, 1) |
() |
| ↓ |
↓ |
| (3, 1) |
(2, 4) |
| ↓ |
↓ |
| () |
(3, 1, 2, 4) |
Sample Input 2
2
1 2
Sample Output 2
1 2
Sample Input 3
8
4 6 3 2 8 5 7 1
Sample Output 3
3 1 2 7 4 6 8 5
The solution above is obtained as follows:
| p |
q |
| (4, 6, 3, 2, 8, 5, 7, 1) |
() |
| ↓ |
↓ |
| (4, 6, 3, 2, 7, 1) |
(8, 5) |
| ↓ |
↓ |
| (3, 2, 7, 1) |
(4, 6, 8, 5) |
| ↓ |
↓ |
| (3, 1) |
(2, 7, 4, 6, 8, 5) |
| ↓ |
↓ |
| () |
(3, 1, 2, 7, 4, 6, 8, 5) |