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

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

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

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