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

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

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

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