Problem: Jafar has n cans of cola. Each can is described by two integers: remaining volume of cola ai and can's capacity bi (ai ≤  bi).

Jafar has decided to pour all remaining cola into just 2 cans, determine if he can do this or not!

Input

The first line of the input contains one integer n (2 ≤ n ≤ 100 000) — number of cola cans.

The second line contains n space-separated integers a1, a2, ..., an (0 ≤ ai ≤ 109) — volume of remaining cola in cans.

The third line contains n space-separated integers that b1, b2, ..., bn (ai ≤ bi ≤ 109) — capacities of the cans.

Output

Print "YES" (without quotes) if it is possible to pour all remaining cola in 2 cans. Otherwise print "NO" (without quotes).

You can print each letter in any case (upper or lower).

Examples

Input

2
3 5
3 6


Output

YES


Input

3
6 8 9
6 10 12


Output

NO


Input

5
0 0 5 0 0
1 1 8 10 5


Output

YES


Input

4
4 1 0 3
5 2 2 3


Output

YES

Note

In the first sample, there are already 2 cans, so the answer is "YES".

Solution (in PYTHON3):

Solution:
from sys import stdin

def two_largest_volume(numbers):
    count = 0
    m1 = m2 = int(0)
    for x in numbers:
        count += 1
        if x > m2:
            if x >= m1:
                m1, m2 = x, m1
            else:
                m2 = x
    return m1 + m2


n = int(stdin.readline())
volumes = [int(elem) for elem in stdin.readline().split()]
capacities = [int(elem) for elem in stdin.readline().split()]
if n <= 1:
  print("NO")
elif n == 2:
  print("YES")
elif two_largest_volume(capacities) >= sum(volumes):
  print("YES")
else:
  print("NO")