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

Example 2:
Input:  1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
Output: 7 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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

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