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

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

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

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