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

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

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

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