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

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

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

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