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 PYTHON):

Solution:
n=int(raw_input())
remaining_volumes=[int(i) for i in raw_input().split()]
capacities=[int(i) for i in raw_input().split()]
sum_to_be_filled=sum(remaining_volumes)
max_amount=max(capacities)
remaining_volume=sum_to_be_filled-max_amount
flag1=True
if remaining_volume<=0:
    flag1=False
    print("YES")
else:
    flag=True
    for i in capacities:
        if i==max_amount and flag:
            flag=False
            continue
        elif i>=remaining_volume:
            print("YES")
            flag1=False
            break

if flag1:
    print("NO")