Nowruz Cup 2015

Soon there will be team competition «Nowruz Cup 2015». The team must consist of exactly two participants. Amanchik wants to participate in it. He found the list of all 2 * n (1 ≤ n ≤ 10^5) participants including himself. Each participant has its own rating. Team rating is the average rating of the two participants. The higher the rating the higher team's place. The team takes place number k + 1 if there is exactly k teams with strictly greater rating.

Of the various partitions find the highest and the lowest place can take Amanchik's team. Amanchik is a participant number 1.

Input

First line contains integer n. Next line contains 2 * n space separated integers a[i] (1 ≤ a[i] ≤ 10^5, 1 ≤ i ≤ 2 * n).

Output

Print two integers - the highest and the lowest place of Amanchik's team.

Examples

Note

In the first example, if we divide the participants in the following way (999, 2) (3, 1) (1000, 1), Amanchik's team (999, 2) and team (1000, 1) will take the first place, and the team (3, 1) will take the third place. If we divide the participants like (999, 1) (1000, 2) (3, 1), Amanchik's team will take second place. Out of the various partitions, the above will meet the highest and lowest places.