Twin Buildings CodeForces

http://codeforces.com/problemset/problem/1252/H

As you might already know, space has always been a problem in ICPC Jakarta. To cope with this, ICPC Jakarta is planning to build two new buildings. These buildings should have a shape of a rectangle of the same size. Now, their problem is to find land to build the buildings.

There are NN lands available for sale. The ithith land has a rectangular shape of size Li×WiLi×Wi. For a good feng shui, the building's side should be parallel to the land's sides.

One way is to build the two buildings on two different lands, one on each land (not necessarily with the same orientation). A building of size A×BA×B can be build on the ithith land if and only if at least one of the following is satisfied:

• A≤LiA≤Li and B≤WiB≤Wi, or
• A≤WiA≤Wi and B≤LiB≤Li.

Alternatively, it is also possible to build two buildings of A×BA×B on the ithith land with the same orientation. Formally, it is possible to build two buildings of A×BA×B on the ithith land if and only if at least one of the following is satisfied:

• A×2≤LiA×2≤Li and B≤WiB≤Wi, or
• A×2≤WiA×2≤Wi and B≤LiB≤Li, or
• A≤LiA≤Li and B×2≤WiB×2≤Wi, or
• A≤WiA≤Wi and B×2≤LiB×2≤Li.

Your task in this problem is to help ICPC Jakarta to figure out the largest possible buildings they can build given NNavailable lands. Note that ICPC Jakarta has to build two buildings of A×BA×B; output the largest possible for A×BA×B.

Input

Input begins with a line containing an integer: NN (1≤N≤1000001≤N≤100000) representing the number of available lands. The next NN lines each contains two integers: LiLi WiWi (1≤Li,Wi≤1091≤Li,Wi≤109) representing the size of the land.

Output

Output in a line a number representing the largest building that ICPC Jakarta can build with exactly one decimal point (see sample input/output for clarity).

Examples

Input

2
5 5
3 4

Output

12.5

Input

2
2 5
4 3

Output

8.0

Input

3
10 1
9 8
7 6

Output

42.0

Note

Explanation for the sample input/output #1

Two buildings of 2.5×52.5×5 can be built both on the first land.

Explanation for the sample input/output #2

Two buildings of 2×42×4 can be built each on the first and second lands.

Explanation for the sample input/output #3

Two buildings of 7×67×6 can be built each on the second and third lands.

巧妙的思维题

#include <bits/stdc++.h>

using namespace std;

struct node
{
    long long x, y;
}a[100005];

bool cmp(struct node a, struct node b)
{
    return a.y > b.y;
}

int main()
{
    int n, i;
    cin >> n;
    long long re = 0;
    for (i = 1; i <= n; i++)
    {
        cin >> a[i].x >> a[i].y;
        re = max(re, a[i].x*a[i].y);
        if(a[i].x > a[i].y) swap(a[i].x, a[i].y);
    }
    sort(a + 1, a + n + 1, cmp);
    long long xx = 0;
    for (int i = 1; i <= n; i++)
    {
        re = max(re, min(xx, a[i].x) * a[i].y * 2);
        xx = max(xx, a[i].x);
    }
    if (re % 2)
        printf("%lld.5
", re / 2);
    else
        printf("%lld.0
", re / 2);
    return 0;
}