<|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:  2 4 5 2 9 0 0 0 0 0 0 9 1 7
Output: 7 2 4 5 2 9 0 0 0 0 0 0 9 1

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

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

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