<|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:  7 2 2 2 5 9 3 5 7 3 7 4 7 2 2 3 0 0 0 0 0 0 0 0 4
Output: 2 2 5 9 3 5 7 3 7 4 7 2 2 3 0 0 0 0 0 0 0 0 4 7 2

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

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

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