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 0 0 0 0 0 0 0 0 0 0 0 0 0 6 5 5 1 9 2 6 9 2 9 1 4 2 1 2
Output: 2 8 0 0 0 0 0 0 0 0 0 0 0 0 0 6 5 5 1 9 2 6 9 2 9 1 4 2 1

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
2 9 3 5 8 3 2 4 2 9 5 5 8 9 2 6 2 0 0 0 0 0 0 0 0 0 0 0 8
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