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

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

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

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