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

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

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

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