E. EZ
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

The secret society UnBalloon has many members, many contacts, and many agreements. Because of a bet lost in rock-paper-scissors during a trip, UnBalloon became responsible for sending, every full moon, a supply of mice to feed the forest witch's pet snake.

In a certain month, the full moon fell on Wednesday, Caleb's day off from work (one of UnBalloon's members). Because of this, he was chosen to deliver the supply of mice, instead of drinking Martinis at the bar as usual. Being very methodical, Caleb decided to take $$$N$$$ mice, where the $$$i$$$-th heaviest of these mice weighs exactly $$$i$$$ kilograms.

When entering the witch's cottage to make the delivery, he heard her saying something about "...not giving wings to the snake...". Perhaps because of that, as soon as she received the supply of mice, she enchanted them as follows: "After eating a mouse weighing $$$i$$$ kilograms, it will not be possible to eat mice weighing $$$i-1$$$ or $$$i+1$$$ kilograms.".

Caleb was astonished by this and thought: "What will then be the greatest total amount, in kilograms, that the snake will be able to eat under this restriction?". To his surprise, the snake heard his thoughts and replied (telepathically): "EZ...". Caleb knows that EZ is an abbreviation of easy. But is eating the greatest possible amount really that easy?

Calculate for Caleb the greatest total amount, in kilograms, that the snake will be able to eat, considering the restriction imposed by the witch's spell.

Input

The input consists of a single line containing a single integer $$$N$$$: the number of mice $$$(1 \leq N \leq 1000)$$$.

Output

Print a single line containing a single integer: the greatest total amount, in kilograms, that the snake can eat in total.

Examples
Input
1
Output
1
Input
3
Output
4
Input
4
Output
6
Input
1000
Output
250500
Note

In the first test case, with only one mouse, the snake will only eat it (total: $$$1$$$ kilogram).

In the second test case, the snake can eat mice weighing $$$1$$$ and $$$3$$$, resulting in $$$4$$$ kilograms eaten (which is the maximum possible).

In the third test case, the snake can eat mice weighing $$$2$$$ and $$$4$$$, resulting in $$$6$$$ kilograms eaten (which is the maximum possible).