Statement

During his algorithmic excursions in the Alps, Giorgio likes to stop from time to time and visit some attractions. An attraction can be any place: an old abandoned church, a safe house or just a remarkable place from which to watch the stunning landscape. He has marked on the map N of these attractions, each situated at a different altitude of A[i] meters above sea level. The night before the excursion, Luca wanted to pull a prank on Giorgio and erased all the altitudes from the map. Instead, he left a footnote with a list of (N * (N-1))/2 numbers where each value is the positive altitude difference between two attractions (reported only once, i.e. for each pair of different attractions (i, j) only the difference |A[i] - A[j]| is listed). Giorgio has just woken up and found the prank: knowing that among the attractions he also listed his house (located at an altitude of zero meters), help him saving his excursion by reconstructing all the altitudes of the attractions!