A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: Find the common rule that maps an input grid to an output grid, given the examples below.

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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
7 2 7 1 7 4 8 3 6 1 9 2 2 4 5 6 8 4 3 3 3 8 2 7 0 0 0 0 0 5
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>.
Assistant: Let me solve this step by step.
<think>
user