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

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

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

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