Problem Statement

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.