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

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

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

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