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

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

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

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