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

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

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

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