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 5 9 4 2 6 5 9 1 6 4 6 6 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output: 9 4 2 6 5 9 1 6 4 6 6 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 5

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

Example 3:
Input:  7 1 4 4 9 3 2 7 1 2 2 7 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output: 4 4 9 3 2 7 1 2 2 7 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 1

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