<|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:  1 5 4 7 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 4
Output: 0 3 4 1 5 4 7 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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

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

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