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 $*a*_{1}, *a*_{2}, ..., *a*_{*n*}$ ($0 ≤ *a*_{*i*} ≤ 10^{9}$) — volume of remaining cola in cans.

The third line contains $*n*$ space-separated integers that $*b*_{1}, *b*_{2}, ..., *b*_{*n*}$ ($*a*_{*i*} ≤ *b*_{*i*} ≤ 10^{9}$) — 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".