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

Example 2:
Input:  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 5 6 2 6 2 2 2 3 0
Output: 2 2 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 5 6 2 6 2

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

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