Ball Coloring

There are N bags, each containing two white balls. The i-th box contains two balls with integers x_i and y_i written on them, respectively.

For each of these bags, you will paint one of the balls red, and paint the other blue.

Afterwards, the 2N balls will be classified according to color.

Then, we will define the following:

• R_{max}: the maximum integer written on a ball painted in red
• R_{min}: the minimum integer written on a ball painted in red
• B_{max}: the maximum integer written on a ball painted in blue
• B_{min}: the minimum integer written on a ball painted in blue

Find the minimum possible value of (R_{max} - R_{min}) \times (B_{max} - B_{min}).

Constraints

• 1 ≤ N ≤ 200,000
• 1 ≤ x_i, y_i ≤ 10^9

Input

Input is given from Standard Input in the following format:

N x_1 y_1 x_2 y_2 : x_N y_N

Output

Print the minimum possible value.

Examples

Input

3 1 2 3 4 5 6

Output

15

Input

3 1010 10 1000 1 20 1020

Output

380

Input

2 1 1 1000000000 1000000000

Output

999999998000000001

inputFormat

Input

Input is given from Standard Input in the following format:

N x_1 y_1 x_2 y_2 : x_N y_N

outputFormat

Output

Print the minimum possible value.

Examples

Input

3 1 2 3 4 5 6

Output

15

Input

3 1010 10 1000 1 20 1020

Output

380

Input

2 1 1 1000000000 1000000000

Output

999999998000000001

样例

2
1 1
1000000000 1000000000

999999998000000001