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

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

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

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 1 4 3 5 5 9 3 3 9 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