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

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

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

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