<|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:  4 1 2 1 3 0 0 0 0 3 9 7 9 5 6 8 2 4 8 6 3 7 2 1 4
Output: 3 0 0 0 0 3 9 7 9 5 6 8 2 4 8 6 3 7 2 1 4 4 1 2 1

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

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

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