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

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

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

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