A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: Find the common rule that maps an input grid to an output grid, given the examples below.

Example 1:
Input:  5 5 2 8 7 0 0 0 0 0 0 0 0 1 7 3 1 2 8
Output: 2 8 7 0 0 0 0 0 0 0 0 1 7 3 1 2 8 5 5

Example 2:
Input:  3 4 9 4 7 6 8 9 3 9 5 1 8 7 0 0 0 9 5
Output: 9 4 7 6 8 9 3 9 5 1 8 7 0 0 0 9 5 3 4

Example 3:
Input:  1 1 3 0 0 3 3 4 7 5 5 6 2 5 9 4 8 2 5
Output: 3 0 0 3 3 4 7 5 5 6 2 5 9 4 8 2 5 1 1

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
5 5 6 1 9 8 2 2 7 5 1 1 4 4 0 0 0 1 6
Show your work in <think> </think> tags, and return the answer in <answer> </answer> tags with space between each number. For example <answer> 1 3 5 7 </answer>.
Assistant: Let me solve this step by step.
<think>
user