<|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 0 0 0 0 1 1 4 6 5 1 4 9 0 0 0 0 0 0 0 0 0 0 0 0 0
Output: 0 0 0 0 1 1 4 6 5 1 4 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
5 4 0 0 0 2 1 9 8 4 9 6 9 1 8 6 1 7 6 5 2 9 5 1 7 6 5 7 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