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

Example 2:
Input:  0 0 0 0 0 0 0 0 0 0 0 0 4 1 1 8 2 4 5 9 0 0 0 0 0 0 0 0
Output: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 1 8 2 4 5 9 0 0 0 0

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

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