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:
a=int(input())
b=raw_input().split(' ')
c=raw_input().split(' ')
d=0
l=0
max1=-99999999
max2=-99999999
for i in range(0,a):
    d=d+int(b[i])
for j in range(0,a):
    if int(c[j])>max1:
        max1=int(c[j])
        l=j
c.pop(l)
for lp in range(0,a-1):
    if int(c[lp])>max2:
        max2=int(c[lp])
if max2+max1>=d:
    print "YES"
if max2+max1<d:
    print "NO"