<|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 6 4 1 0 0 0 0 0 0 0 7 8 9 6
Output: 9 6 7 6 4 1 0 0 0 0 0 0 0 7 8

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

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

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