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

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

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

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