B. Group Photo 2 (online mirror version)
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Many years have passed, and n friends met at a party again. Technologies have leaped forward since the last meeting, cameras with timer appeared and now it is not obligatory for one of the friends to stand with a camera, and, thus, being absent on the photo.

Simply speaking, the process of photographing can be described as follows. Each friend occupies a rectangle of pixels on the photo: the i-th of them in a standing state occupies a w i pixels wide and a h i pixels high rectangle. But also, each person can lie down for the photo, and then he will occupy a h i pixels wide and a w i pixels high rectangle.

The total photo will have size W × H, where W is the total width of all the people rectangles, and H is the maximum of the heights. The friends want to determine what minimum area the group photo can they obtain if no more than n / 2 of them can lie on the ground (it would be strange if more than n / 2 gentlemen lie on the ground together, isn't it?..)

Help them to achieve this goal.

Input

The first line contains integer n (1 ≤ n ≤ 1000) — the number of friends.

The next n lines have two integers w i, h i (1 ≤ w i, h i ≤ 1000) each, representing the size of the rectangle, corresponding to the i-th friend.

Output

Print a single integer equal to the minimum possible area of the photo containing all friends if no more than n / 2 of them can lie on the ground.

Examples
Input
310 120 230 3
Output
180
Input
33 12 24 3
Output
21
Input
15 10
Output
50