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

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

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