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

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

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

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