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

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

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

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