Villages on a Highway

Several villages lie in a row along a straight highway. The highway has no junctions, so all villages sit in order on a single line.

If you know the distances between neighbouring villages, you can compute the distance between any two villages. For example, if five villages A, B, C, D, E lie in a row and the neighbouring distances are given, you can build the full table of pairwise distances — $N(N-1)/2$ of them in total.

Now consider the reverse: given all $N(N-1)/2$ pairwise distances, write a program that determines the order of the villages and recovers the $N-1$ distances between neighbouring villages. Several arrangements may produce the same set of distances; in that case you must find all of them.

The input consists of several test cases. The first line of each test case contains the number of villages $N$ ($2 \le N \le 20$). It is followed by the $N(N-1)/2$ pairwise distances, given as integers separated by spaces or newlines in non-increasing (descending) order. Each distance is a natural number between $1$ and $400$ inclusive, and the largest distance is the one between the leftmost and the rightmost village.

The last line contains a single $0$, which marks the end of the input.

For each test case, print the $N-1$ distances between neighbouring villages, separated by spaces. If several answers exist, regard each answer as a sequence of distances, sort the sequences lexicographically, and print them all, one per line. If no answer is possible, print nothing. After printing all answers of a test case, print ----- on its own line.