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

Example 2:
Input:  7 9 7 0 0 0 0 0 0 0 7 2 5 5 9
Output: 9 7 0 0 0 0 0 0 0 7 2 5 5 9 7

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

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