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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
2 6 7 3 9 0 0 0 0 0 0 0 8 1 2 4 7 4 2 8 8 5 7 7 1 2 5
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