Jafar has n cans of cola. Each can is described by two integers: remaining volume of cola a**i and can's capacity b**i (a**i  ≤  b**i).

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, ..., a**n (0 ≤ a**i ≤ 109) — volume of remaining cola in cans.

The third line contains n space-separated integers that b1, b2, ..., b**n (a**i ≤ b**i ≤ 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).

Note

In the first sample, there are already 2 cans, so the answer is "YES".

Samples

2
3 5
3 6

YES

3
6 8 9
6 10 12

NO

5
0 0 5 0 0
1 1 8 10 5

YES

4
4 1 0 3
5 2 2 3

YES