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

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

Example 3:
Input:  2 4 4 7 3 4 3 4 6 3 7 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output: 5 7 3 6 4 3 4 3 7 4 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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 1 5 7 3 2 0 0 0 0 0 0 0 0 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