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

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

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

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