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

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

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

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