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:  8 1 2 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 3 1 6 3 3 9 8 1
Output: 8 1 8 1 2 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 3 1 6 3 3 9

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
5 5 2 5 4 1 7 5 2 6 5 7 8 2 3 4 9 2 8 6 5 7 4 5 5 1
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