Young Maids

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.

Examples

Input

4 3 2 4 1

Output

3 1 2 4

Input

2 1 2

Output

1 2

Input

8 4 6 3 2 8 5 7 1

Output

3 1 2 7 4 6 8 5

inputFormat

Input

Input is given from Standard Input in the following format:

N p_1 p_2 ... p_N

outputFormat

Output

Print the lexicographically smallest permutation, with spaces in between.

Examples

Input

4 3 2 4 1

Output

3 1 2 4

Input

2 1 2

Output

1 2

Input

8 4 6 3 2 8 5 7 1

Output

3 1 2 7 4 6 8 5

样例

2
1 2

1 2