Recently I solved an interesting constructive task. Can you solve it? I'll reveal the source a bit later.

N(N + 1) soccer players stand in a row. The height of the i-th player is h_i. No two of them are of the same height.

Sir Alex wants to remove N(N−1) players from this row leaving a new row of 2N players in which the following N conditions hold:

• No one stands between the two tallest players,
• No one stands between the third and fourth tallest players,
• 
• No one stands between the two shortest players.

Find one possible way to achieve this.

Constraints: 2 ≤ N ≤ 500, 1 ≤ h_i ≤ 10⁹, h_i are pairwise distinct.