A. Greed
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 a 1, a 2, ..., a n (0 ≤ a i ≤ 109) — volume of remaining cola in cans.

The third line contains n space-separated integers that b 1, b 2, ..., 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).

Examples
Input
23 53 6
Output
YES
Input
36 8 96 10 12
Output
NO
Input
50 0 5 0 01 1 8 10 5
Output
YES
Input
44 1 0 35 2 2 3
Output
YES
Note

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