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:
from __future__ import print_function
"""import math
n=(input()) 
#print "number is %.2f" %n
print math.floor(n*100)/100        """ 
#!/bin/python
#print math.log(n,2)               
from itertools import combinations

"""n=5
a=[3,6,7,8]
b=[i>n for i in a]

if sum(b)>0:
 print("YES")
else:
 print("NO")       """
                  

n=int(input())
a=[]
for i in range(2):
 e=map(int,raw_input().split())
 a.append(e)

sa=sum(a[0])
s=[]
f=0
a[1].sort()
c=a[1][len(a[1])-1]
d=a[1][len(a[1])-2]
#print(c+d)
if c+d>=sa:
 print("YES")
else:
 print("NO")
"""for i in combinations(a[1],2):
 s.append(sum(i))
 if sum(i)>=sa:
  f=1
  print("YES")
  break

if not f:
 print("NO")           """

"""s.sort()
ma=s[len(s)-1]

if ma>=sa:
 print("YES")
else:
 print("NO")       """