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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
7 1 3 1 9 2 8 7 1 2 7 1 2 4 5 3 9 9 0 0 0 0 0 0 0 3 9 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