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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
3 1 7 7 9 9 4 5 5 2 3 7 4 7 1 4 8 5 3 3 2 5 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