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 read1():
    ent = input()
    line = input().split()
    b = input().split()
    return list(map(int, line)), list(map(int, b))

def f1(a,b):
    m1, m2 = 0, 0
    ind = -1
    for i in range(len(b)):
        if m1 <= b[i]:
            m1 = b[i]
            ind = i
    b[ind] = -1
        
    if max(b) + m1 >= sum(a):
        return 'YES'
    return 'NO'

a = [1,1,1, 2]
b = [3,1,1, 2]
#print(f1(a,b))
print(f1(*read1()))