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())
n2=input()
n2+=" "
n3=input()
n3+=" "
kol = ''
n4 = 0
n5 = []
for i in range(0, len(n2)):
    if (n2[i]!=" "):
        kol+=n2[i]
    if (n2[i]==" "):
        n4+=int(kol)
        kol=""
for i in range(0, len(n3)):
    if (n3[i]!=" "):
        kol+=n3[i]
    if (n3[i]==" "):
        n5.append(int(kol))
        kol=""
kol = 0
max = 0
elim = 0
for i in range(0, 2):
    for i in range(0, n):
        if (n5[i]>max):
            max=n5[i]
            elim = i
    kol+=max
    max = 0
    n5.pop(elim)
    n-=1
if (kol >= n4):
    print("YES")
elif(kol < n4):
    print("NO")