Practice Combinatorics with the exercise "Crack the Trio Code"

Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

Combinatorics

Statement

Goal

There are three positive integers, called triads. By selecting 1 to 3 of these numbers (with repetitions allowed) and summing them, you obtain what is known as triad sums. You are given a sorted subset L of triad sums. Your task is to determine the original triads.
- If there is only one possible set of triads, output them in ascending order (comma-separated).
- If there are multiple possible sets, output many.
- If no valid set exists, output none.

Input

Line 1: A comma-separated list of integers representing a sorted subset of triad sums (with no duplicates).

Output

Line 1: The answer as specified in the statement.

Constraints

max(L) ≤ 120

Example

Input

3,11,12,102,111,120

Output

1,10,100

Solve it

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