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

Example 2:
Input:  0 0 0 1 2 6 4 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output: 2 6 4 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

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

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