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

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

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

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 0 0 0 7 9 4 0 0 0 0 0 0 0 0 0
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