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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
8 6 1 1 5 3 5 1 3 3 7 2 0 0 0 0 1 4 4 8 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