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

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

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