Star Catalog Minimum Magnitude Gap

An observatory catalogs n stars, each with a distinct brightness magnitude (an integer). Astronomers want to know which pairs of catalogued stars are closest together in magnitude. Find the minimum absolute difference between the magnitudes of any two stars in the catalog, then list every pair of stars whose magnitudes differ by exactly that minimum amount. Each pair should be listed as its smaller magnitude followed by its larger magnitude, and the pairs themselves should be listed in increasing order of their smaller magnitude.

Input format

Line 1: an integer n, the number of stars. Line 2: n space-separated integers, the distinct magnitudes of the stars, in no particular order.

Output format

One line per qualifying pair, each containing the pair's smaller magnitude then its larger magnitude, separated by a single space, ordered by increasing smaller magnitude. Print nothing else.

Constraints

• 2 <= n <= 100000
• -1000000 <= magnitude <= 1000000
• All n magnitudes are distinct.

4
4 2 1 3

1 2
2 3
3 4

5
1 3 6 10 15

1 3