Kristýna chose a certain odd natural number divisible by three. Jakub and David then examined triangles whose perimeter in millimeters was equal to the number chosen by Kristýna and whose sides had lengths in millimeters expressed by different whole numbers.

Jakub found such a triangle in which the longest side had the greatest possible length, and he wrote this value on the board. David found such a triangle in which the shortest side had the greatest possible length, and he also wrote this value on the board. Kristýna correctly added both lengths on the board, and it came to $1681 \mathrm{~mm}$.

Determine which number Kristýna chose.

(L. Růžičková)

Hint. Can you, given the described property of Kristýna's number, express Jakub's and David's numbers?

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