Predicting the Next Appearance of Lanbao

On April 12, 2025, just before the provincial contest, the mascot Lanbao went missing again! Little Lan discovered from the activity log that Lanbao’s appearances are closely related to two important dates of the Blue Bridge Cup:

• The 16th provincial contest date: \(20250412\).
• The 15th provincial contest date: \(20240413\).

After analysis, Little Lan conjectures that the next appearance time \(N\) of Lanbao is the smallest positive integer satisfying:

1. \(N + 20250412\) is divisible by \(20240413\), i.e. \(20240413 \mid (N+20250412)\).
2. \(N + 20240413\) is divisible by \(20250412\), i.e. \(20250412 \mid (N+20240413)\).

It can be shown that these conditions lead to a unique minimal solution given by \[ N = 20250412 \times 20240413 - (20250412 + 20240413). \]

Your task is to compute and output this number \(N\).

inputFormat

This problem does not require any input.

outputFormat

Output the smallest positive integer (N) that satisfies the conditions.

sample

409876682049743