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

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

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

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