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:  9 1 4 0 0 0 0 0 7 8 8 9 3 9 7 2 6 6 9 7 6 7 6 8 6 8 8 6
Output: 4 0 0 0 0 0 7 8 8 9 3 9 7 2 6 6 9 7 6 7 6 8 6 8 8 6 9 1

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
3 4 1 0 0 0 0 3 5 7 1 9 8 1 2 2 6 7 7 2 9 6 6 1 5 6 4 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