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

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

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

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