Greed

Description:

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).

Sample Input:

2
3 5
3 6

Sample Output:

YES

Sample Input:

3
6 8 9
6 10 12

Sample Output:

NO

Sample Input:

5
0 0 5 0 0
1 1 8 10 5

Sample Output:

YES

Sample Input:

4
4 1 0 3
5 2 2 3

Sample Output:

YES

Note:

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