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
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

Source: codeforces | Difficulty: HARD
Tags: Complete search

Sorting

Greedy algorithms


Solutions:
from operator import neg
n = int(input())
a = [tuple(map(int, input().split())) for i in range(n)]

def check(max_h):
	k = n // 2
	b = []
	for (w, h) in a:
		if h > max_h:
			if k <= 0 or w > max_h:
				return 1 << 60
			b.append((h, w))
			k -= 1
		else:
			b.append((w, h))
	b.sort(key=lambda t: t[1] - t[0])
	r = 0
	for (w, h) in b:
		if k > 0 and w <= max_h and (h < w):
			r += h
			k -= 1
		else:
			r += w
	return r * max_h
print(min((check(h) for h in range(1, 1001))))