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

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

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

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