<|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:  0 0 0 0 7 8 7 3 4 7 3 5 2 9 7 4 9 6 7 0 0
Output: 7 0 0 0 0 0 0 7 8 7 3 4 7 3 5 2 9 7 4 9 6

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
3 1 4 3 8 4 4 9 2 8 9 4 3 1 3 5 6 7 4 9 8
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