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:
def solve(a, b, n):
    if n == 2:
        return "YES"
    a = sorted(a, reverse=True)
    b = sorted(b, reverse=True)
    empty = b[0] - a[0] + b[1] - a[1]
    if sum(a[2:]) > empty:
        return "NO"
    return "YES"


def main():
    # vars = list(map(int, input().split(" ")))
    n = int(input())
    a = list(map(int, input().split(" ")))
    b = list(map(int, input().split(" ")))
    # for i in range(n):
    #     arr.append(list(map(int, list(input()))))
    print(solve(a, b, n))


main()