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

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

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

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