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

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

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

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