The Least Common Multiple#1655

The Least Common Multiple

1 second

128 megabytes

Very easy

Find the least common multiple of all integers from $1$ to $n$ .

The least common multiple of positive integers $a_{1}, a_{2}, \dots, a_{k}$ a_1, a_2, \ldots, a_k is a number $A$ such that $A$ is divisible by each $a_{i}$ a_i for all $i$ from $1$ to $k$ , and $A$ is the smallest positive integer with this property.

Input

One integer $n$ ( $1 \leq n \leq 1000$ 1 \le n \le 1000).

Output

Output one integer — the least common multiple of all integers from $1$ to $n$ .

Examples

Example 1

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a_{1}, a_{2}, \dots, a_{k}

a_{i}

1 \leq n \leq 1000