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:
def solve():
    n = input()
    a = map(int, raw_input().split())
    b = map(int, raw_input().split())

    from collections import Counter 
    c = Counter(b)
    s = sum(a)
    b.sort()

    def solve(elem):

        lft = 0
        rgt = len(b) - 1

        ans = -1
        while lft <= rgt:
            mid = (lft + rgt) >> 1
            if b[mid] >= elem:
                ans = mid
            lft = mid + 1
        return ans 

    for i in b:
        remain = s - i
        res = solve(remain)
        if res == -1:
            continue 
        res = b[res]

        if i == res and c[res] < 2:
            continue
        return "YES"
    return "NO"
print solve()