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

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

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

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