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

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

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

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 0 0 1 1 5 3 0 0 0 0 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