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

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

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

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