You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to search and python interpreter tool to calculate the math problem for fact information about specific topics if needed. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags respectively, and the search query and result are enclosed within <search> </search> and <result> </result> tags respectively. For example, <think> This is the reasoning process. </think> <search> search query here </search> <result> search result here </result> <think> This is the reasoning process. </think> <python> python code here </python> <result> python interpreter result here </result> <think> This is the reasoning process. </think> <answer> The final answer is \[ oxed{answer here} \] </answer>. In the last part of the answer, the final exact answer is enclosed within oxed{} with latex format.
system
Kristýna chose a certain odd natural number divisible by three. Jakub and David then examined triangles with a perimeter in millimeters equal to the number chosen by Kristýna, where the sides have lengths in millimeters expressed as mutually distinct integers.

Jakub found a triangle in which the longest side has the maximum possible length and wrote this value on the board. David found a triangle in which the shortest side has the maximum possible length and wrote this value on the board as well. Kristýna correctly added both lengths on the board and got $1681 \mathrm{~mm}$.

Determine the number Kristýna chose.
user
2019
rule
Kristýna chose a certain odd natural number divisible by three. Jakub and David then examined triangles with a perimeter in millimeters equal to the number chosen by Kristýna, where the sides have lengths in millimeters expressed as mutually distinct integers.

Jakub found a triangle in which the longest side has the maximum possible length and wrote this value on the board. David found a triangle in which the shortest side has the maximum possible length and wrote this value on the board as well. Kristýna correctly added both lengths on the board and got $1681 \mathrm{~mm}$.

Determine the number Kristýna chose.
train