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

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

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

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