Problem: 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".

Solution (in PYTHON):

Solution:
def main():
	n = raw_input()
	input_line2 = raw_input().split()
	input_line3 = raw_input().split()
	input_line3 = sorted(map(lambda x : int(x),input_line3),reverse=True)
	total_cola  = sum(map(lambda x : int(x),input_line2))
	cap_two = input_line3[0]+input_line3[1]
	if total_cola > cap_two:
		print("NO")
	else:
		print("YES")
	#remaining   = sorted([j-1 for i,j in zip(input_line3,input_line2)],reverse=True)
	
		
		

if __name__=='__main__':
	main()