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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
9 6 2 2 8 6 6 3 4 9 5 9 7 4 6 8 7
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