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# Given the number of animals and the required distance pairs of certain animals, write a program that prints a satisfying solution or informs the user that there is none if a solution does not exist.

INSTRUCTIONS TO CANDIDATES

Story

The animals are still making too much noise. Some animals antagonize nearby animals and cause them to emit screams of rage or cries of annoyance. However, some animals want to be nearby other particular animals or they emit cries of longing. You have experimented with different animals at different distances from each other. You have made some notes, and to make your life easier you have represented each animal with a unique natural number index. Now you feel that you now have enough information to move forward with your new plans.

The animals will be in a line of exhibits. Each animal will be in its own exhibit, and there are an equal number of animals as exhibits. You have found that certain pairs of animals need to be exactly some distance from each other. You want to find out if there is an arrangement of animals that satisfies all the required distances.

Problem

Given the number of animals and the required distance pairs of certain animals, write a program that prints a satisfying solution or informs the user that there is none if a solution does not exist.

Input

Input will begin with a line containing 2 integers, n and c (1 ≤ n ≤ 20; 0 ≤ c ≤ n choose 2), representing the number of animal exhibits and the number of constraints. The following c lines will each contain a constraint description in the form of 3 space separated integers, f, s, and d (1 ≤ f, s ≤ n; f ≠ s; 0 ≤ c ≤ n - 2), representing the index of the first animal, the index of the second animal, and the exact number of cages that should be in between those 2 animals.

For 7 of the 10 cases each animal will be in at most 1 constraint.

Output

Output should contain 1 line. In the event that a solution exists, you should print out n space separated integers representing the animal index given in order from the first cage to the last. If there is no solution the output should be only the phrase “No Solution.” (quotes for clarity).

(5/5)

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