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

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

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

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