Maximize the Ratio#10174

Maximize the Ratio

1 second

128 megabytes

Very easy

Consider the function $R (x)$ defined for positive integers $x$ as $R (x) = \frac{x}{S ( x )}$ R(x) = \frac{x}{S(x)}, where $S (x)$ is the sum of all divisors of $x$ . For example, $R (6) = \frac{6}{1 + 2 + 3 + 6} = 0.5$ R(6) = \frac{6}{1 + 2 + 3 + 6} = 0.5, $R (7) = \frac{7}{1 + 7} = 0.875$ R(7) = \frac{7}{1 + 7} = 0.875.

Given $n$ , find an integer $x \leq n$ x \leq n such that $R (x)$ is maximal. If there is more than one such integer, choose the largest one.

Input

The input contains one integer $n$ ( $1 \leq n \leq 1 0^{5}$ 1 \leq n \leq 10^5).

Output

Print one integer $x$ : the answer to the problem.

Examples

Example 1

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R (x) = \frac{x}{S ( x )}

R (6) = \frac{6}{1 + 2 + 3 + 6} = 0.5

R (7) = \frac{7}{1 + 7} = 0.875

x \leq n

1 \leq n \leq 1 0^{5}