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

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

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

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