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

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

Example 3:
Input:  7 3 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 7 1 1
Output: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 7 1 1 7 3 8

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