<|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:  3 5 4 4 4 9 1 8 8 4 6 9 4 2 5 3 9 9 6 6 6 9 7 0 0 0 0 0 8
Output: 5 4 4 4 9 1 8 8 4 6 9 4 2 5 3 9 9 6 6 6 9 7 0 0 0 0 0 8 3

Example 2:
Input:  5 1 2 4 8 4 6 7 0 0 0 0 0 0 0 0 0 0 2 9 2 9 4 3 2 7 8 5 9
Output: 1 2 4 8 4 6 7 0 0 0 0 0 0 0 0 0 0 2 9 2 9 4 3 2 7 8 5 9 5

Example 3:
Input:  8 6 7 9 6 4 2 5 3 5 8 2 9 7 1 0 0 0 0 5 5 7 6 5 7 1 4 6 9
Output: 6 7 9 6 4 2 5 3 5 8 2 9 7 1 0 0 0 0 5 5 7 6 5 7 1 4 6 9 8

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
2 1 7 8 8 6 4 9 1 6 6 2 3 2 1 6 8 2 5 3 1 5 2 9 9 6 0 0 1
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