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

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

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

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