<|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:  7 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 7 0 0

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
0 0 7 1 1 8 8 1 2 1 6 6 1 1 9 5 4 9 3 4 5 5 6 7 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