<|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:  1 6 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 2 1 6
Output: 2 1 6 1 6 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2

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

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

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