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:

n=int(input())
r=list(map(int,input().split()))
l=list(map(int,input().split()))
a=sum(r)
ma=max(l)
ma1=max(l[0],l[1])
ma2=min(l[1],l[0])
for i in range(len(l)):
	if l[i]>ma1:
		ma2=ma1
		ma1=l[i]
		
	elif l[i]<ma1 and l[i]>ma2:
		ma2=l[i]
	elif l[i]<ma2:
		continue

d=ma+ma2
# print(d)
if d>=a:
	print('YES')
else:
	print('NO')