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

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

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

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