#D8030. Group Photo 2 (online mirror version)
Group Photo 2 (online mirror version)
Group Photo 2 (online mirror version)
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 wi pixels wide and a hi pixels high rectangle. But also, each person can lie down for the photo, and then he will occupy a hi pixels wide and a wi 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 wi, hi (1 ≤ wi, hi ≤ 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
3 10 1 20 2 30 3
Output
180
Input
3 3 1 2 2 4 3
Output
21
Input
1 5 10
Output
50
inputFormat
Input
The first line contains integer n (1 ≤ n ≤ 1000) — the number of friends.
The next n lines have two integers wi, hi (1 ≤ wi, hi ≤ 1000) each, representing the size of the rectangle, corresponding to the i-th friend.
outputFormat
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
3 10 1 20 2 30 3
Output
180
Input
3 3 1 2 2 4 3
Output
21
Input
1 5 10
Output
50
样例
3
10 1
20 2
30 3
180