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

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

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

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