<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer.<|im_end|>
<|im_start|>user
Find the common rule that maps an input grid to an output grid, given the examples below.

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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
0 0 0 0 0 0 0 0 0 9 2 9 1 2 0 0 0 0 0 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>.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user