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:
kolvo_banok = input()
obiem_koly = input()
obiem_banok  = input()

def search_max(a):
	maxx = int(a[0])
	index = 0
	for i in range(len(a)):
		if maxx<int(a[i]):
			maxx = int(a[i])
			index = i
	return(index)

obiem_banok = obiem_banok.split(' ')
obiem_koly = obiem_koly.split(' ')

index = search_max(obiem_banok)
max1 = int(obiem_banok[index])
del obiem_banok[index]
index = search_max(obiem_banok)
max2 = int(obiem_banok[index])

v = 0
for i in range(len(obiem_koly)):
	v = v+int(obiem_koly[i])

if (max1+max2)<v:
	print('NO')
else:
	print('YES')