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

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

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

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 9 7 9 4 0 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