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".

Greed