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

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

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

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