3Sum: All Unique Triplets

Northgate Clearing ends every day with a list of ledger adjustments, some positive and some negative. Before the books close, an auditor has to report each set of three adjustments that wipes each other out — three amounts adding up to nothing at all. Two findings built from the same three amounts are one finding, however those amounts were written down.

Task: Print every distinct trio of amounts that adds up to 0.

Input

A single line holding up to 500 integers separated by single spaces. Values may repeat and may be negative. An amount can be used only as often as it appears, so a line carrying one 0 cannot produce the trio 0 0 0.

Output

One trio per line: three integers separated by single spaces, written smallest first. Order the lines by their first number, and where two share a first number, by their second. A trio holding the same three amounts as an earlier line must not print again. If no trio adds up to 0, print nothing at all.

Example:

Input:
-1 0 1 2 -1 -4

Output:
-1 -1 2
-1 0 1