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

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

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

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