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

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

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

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