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:
number = int(input())
numerator = 0
denominator = 0
lst = list(map(int,input().split()))
lst2 = list(map(int,input().split()))
if len(lst) == 2 and len(lst2) == 2:
	num = 0
	den = 0
	for item in lst:
		num = num + item
	for item in lst2:
		den = den + item
	if den == 0:
		print("YES")
	elif num/den<=1:
		print("YES")
	else:
		print("NO")
else:
	numerator = 0
	for item in lst:
		numerator = numerator + item	
	second = lst2[0]
	for i in range(2):
		for item in lst2:
			if item > second:
				second = item
		denominator = denominator + second
		lst2.remove(second)
		second = lst2[0]
	if denominator == 0:
		print("YES")
	elif numerator/denominator<=1:
		print("YES")
	else:
		print("NO")