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

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

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

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