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

Example 2:
Input:  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 7 6
Output: 0 9 7 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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

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