<|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 1 1 1 4 8 3 7 7 3 5 1 4 8 9 2 2 7 7 0 0 0 0 0 6 9
Output: 1 4 8 3 7 7 3 5 1 4 8 9 2 2 7 7 0 0 0 0 0 6 9 1 1 1

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

Example 3:
Input:  3 9 9 5 7 1 7 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
Output: 5 7 1 7 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 3 9 9

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