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A. Greed

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputJafar 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).

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".

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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