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

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

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

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