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

Example 2:
Input:  0 0 0 0 0 0 0 0 0 0 0 0 3 2 1 3 8 4 8 1 9 0 0 0 0 0 0 0 0 0
Output: 0 0 0 0 0 0 0 0 3 2 1 3 8 4 8 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0

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

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