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

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

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

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