Problem:
Score : 800 points

Problem Statement

Let N be a positive even number.

We have a permutation of (1, 2, ..., N), p = (p_1, p_2, ..., p_N).
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 × 10^5

p is a permutation of (1, 2, ..., N).

Input

Input is given from Standard Input in the following format:

N
p_1 p_2 ... p_N

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)

Solution in Python (2.7.6) (judge verdict: Time Limit Exceeded)

raw_input()
l = map(int, raw_input().split())
memo = {}
 
def get_min(l):
    if (l[0], l[-1]) in memo:
        return memo[(l[0], l[-1])]
    r = [(_, idx) for idx, _ in enumerate(l) if idx % 2 == 0]
    first_val, first_idx = min(r)
    r = [(_, idx) for idx, _ in enumerate(l) if idx % 2 != 0 and idx > first_idx]
    second_val, second_idx = min(r)
    ret = (first_val, first_idx, second_val, second_idx)
    memo[(l[0], l[-1])] = ret
    return ret
 
ls = [l]
while (len(ls) > 0):
    first_val = -1
    for lidx, l in enumerate(ls):
        _first_val, _first_idx, _second_val, _second_idx = get_min(l)
        if _first_val < first_val or first_val < 0:
            first_val, first_idx, second_val, second_idx = get_min(l)
            _lidx = lidx
    print first_val, second_val,
    _l = ls.pop(_lidx)
    if first_idx > 0:
        ls.append(_l[:first_idx])
    if first_idx + 2 < second_idx:
        ls.append(_l[first_idx + 1:second_idx])
    if second_idx + 1< len(_l):
        ls.append(_l[second_idx + 1:])
 
print