D. Multiplication Table
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Chisato has an $$$N \times N$$$ multiplication table. A multiplication table is an $$$N \times N$$$ matrix where on cell $$$(i, j)$$$ the number $$$i \cdot j$$$ is written for all $$$i \in [{1 \cdots N}]$$$ and $$$j \in [{1 \cdots N}]$$$.

A $$$3 \times 3$$$ mulitplication table looks like this:

$$$$$$ 1, 2, 3 \\ 2, 4, 6 \\ 3, 6, 9 $$$$$$

Takina challenges her to find the smallest positive number that is not present in the multiplication table. Chisato knows how to find the answer, but do you?

Input

The input is one integer $$$N$$$, denoting the dimensions of the multiplication table $$$(1 \lt N \leq 10^5)$$$.

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Testcases in the subtasks are numbered from $$$1 - 20$$$ with samples skipped.

For testcases $$$1 - 10$$$, $$$1 \lt n \leq 3366$$$.

The remaining testcases do not satisfy any additional constraints.

Output

Output one integer $$$x$$$, the minimum positive integer that is not on the multiplication table.

Examples
Input
3
Output
5
Input
3366
Output
3371
Note

A $$$3 \times 3$$$ multiplication table is present in the statement. As can be observed, there is no $$$5$$$ anywhere on it but all other numbers from $$$1 - 4$$$ are present.

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Idea: 3366

Preparation: 3366

Occurrences: Novice 4