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

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

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