The Fate Between Master and Disciple

One Zen (一禅) wonders about the strength of his fate with his master (师父). To decide this, they agree on a positive integer \( n \). Then each secretly chooses a positive integer not exceeding \( n \). Zen believes that the larger the least common multiple (LCM) of the two chosen numbers, the stronger the bond between him and his master.

The master is curious to know: what is the maximum possible LCM when both choose their numbers optimally?

Note: When \( n = 1 \), the only possible number is 1, so the answer is 1. For \( n \ge 2 \), the maximum LCM is attained by choosing \( n \) and \( n-1 \) since consecutive integers are coprime. Hence, the answer is \( n \times (n-1) \).

inputFormat

The input consists of a single integer \( n \) (\( 1 \le n \le 10^9 \)).

outputFormat

Output a single integer representing the maximum possible least common multiple (LCM) between any two positive integers not exceeding \( n \).

sample

1

1