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

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

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

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