#D5496. Greed
Greed
Greed
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".
inputFormat
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.
outputFormat
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".
样例
4
4 1 0 3
5 2 2 3
yes