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:
a = int(input())


def ls(spis):
    length = len(spis)
    i = 0
    im = 0
    mx = int(spis[i])
    while i < length:
        if mx < int(spis[i]):
            mx = int(spis[i])
            im = i
        i += 1
    return im
if a != 2:
    b = input().split()
    c = input().split()
    length = len(b)
    sum = 0
    i = 0
    while i < length:
        sum += int(b[i])
        i += 1
    i = 0
    sum2 = 0
    f = int(c[ls(c)])
    sum2 += f
    c.remove(str(f))
    f = int(c[ls(c)])
    sum2 += f
    if sum2 >= sum:
        print("Yes")
    else:
        print("No")


else:
    print("Yes")