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

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

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

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