p03735 AtCoder Regular Contest 073 - 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
```python
import sys
from operator import itemgetter
 
inf = 1 << 30
 
def solve():
    n = int(sys.stdin.readline())
 
    # r_max = MAX, b_min = MIN にしたとき
 
    r_max = b_max = 0
    r_min = b_min = inf
 
    p = []
 
    for i in range(n):
        xi, yi = map(int, sys.stdin.readline().split())
 
        if xi > yi:
            xi, yi = yi, xi
 
        p.append((xi, yi))
 
        r_max = max(r_max, yi)
        r_min = min(r_min, yi)
        b_max = max(b_max, xi)
        b_min = min(b_min, xi)
 
    ans1 = (r_max - r_min) * (b_max - b_min)

    # print('r_max = MAX, b_min = MIN -> ', ans1, file=sys.stderr)
 
    # r_max = MAX, r_min = MIN にしたとき
 
    ans2 = (r_max - b_min)
 
    p.sort(key=itemgetter(0))

    # print(*p, sep='\n', file=sys.stderr)
 
    b_min = p[0][0]
    b_max = p[-1][0]
 
    y_min = inf
 
    dif_b = b_max - b_min
 
    for i in range(n - 1):
        if p[i][1] == r_max:
            break
 
        y_min = min(y_min, p[i][1])
 
        b_min = min(p[i + 1][0], y_min)
        b_max = max(b_max, p[i][1])

        # print(b_min, b_max, b_max - b_min, file=sys.stderr)
 
        dif_b = min(dif_b, b_max - b_min)
 
        if y_min < p[i + 1][0]:
            break
 
    ans2 *= dif_b

    # print('r_max = MAX, r_min = MIN ->', ans2, file=sys.stderr)
 
    ans = min(ans1, ans2)
 
    print(ans)
 
if __name__ == '__main__':
    solve()
```