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

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

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

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