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

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

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

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