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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
5 5 7 0 0 0 0 0 0 0 9 9 6 1 8 4 8 1 6 5 2 6 5 3 1 5
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