<|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 0 1 8 5 1 2 3 2 7 7 4 9 6 8 1 2 9 7 9 3 5 1 5 8 3 2 8 6
Output: 8 6 6 0 1 8 5 1 2 3 2 7 7 4 9 6 8 1 2 9 7 9 3 5 1 5 8 3 2

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
2 1 3 5 1 6 7 9 6 4 3 4 1 7 9 2 9 9 7 0 0 0 0 0 0 0 6 6 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