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

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

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

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