Antiprime Numbers

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Problem

A positive integer is called an antiprime (also known as a highly composite number) if it has strictly more divisors than every positive integer smaller than it. For example, 1,2,4,6,12,241, 2, 4, 6, 12, 24 are all antiprimes.

Given an integer nn, write a program that finds the largest antiprime that is not greater than nn.

Input

The first line contains a single integer nn (1n20000000001 \le n \le 2000000000).

Output

Print, on a single line, the largest antiprime that is not greater than nn.