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

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

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

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