Sequence of multiples#7505

Sequence of multiples

3 seconds

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Medium

In the sequence of natural numbers $A_{1}$ A_1, $A_{2}$ A_2, $A_{3}$ A_3,..., each term $A_{k}$ A_k is defined as the smallest natural number that is divisible by all of the first $k$ natural numbers: $1, 2, 3, \dots, k$ 1, 2, 3, \ldots, k. Given a natural number $N$ , determine the smallest $k$ such that the sequence contains $N$ consecutive identical numbers starting from $A_{k}$ A_k.

Input

A natural number $N$ ( $N < 100$ N < 100).

Output

The smallest $k$ for which the sequence has $N$ consecutive identical terms starting from $A_{k}$ A_k.

Examples

Example 1

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A_{1}

A_{2}

A_{3}

A_{k}

1, 2, 3, \dots, k

A_{k}

N < 100

A_{k}