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

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

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

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 7 1 7 7 8 1 6 3 5 8 1 6 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