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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
3 1 0 7 7 0 7 0 2 1 9 0 8 1 4 1 0 4 2 1 6 2 3 0 5 0 9 0 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