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 PYTHON3):

Solution:
def main():
    n = lie()
    a, b = array(), array()
    b.sort(reverse=True)
    cnt = sum(a)
    if cnt <= b[1] + b[0]:
        print('YES')
    else:
        print('NO')


def fun(m, n, s, k):
    return


def fun2(s):
    return


from sys import *
import inspect
import re
from math import *
import threading
from collections import *
from pprint import pprint as pp
mod = 998244353
MAX = 10**5


def lie():
    return int(input())


def liee():
    return map(int, input().split())


def array():
    return list(map(int, input().split()))


def deb(p):
    for line in inspect.getframeinfo(inspect.currentframe().f_back)[3]:
        m = re.search(r'\bdeb\s*\(\s*([A-Za-z_][A-Za-z0-9_]*)\s*\)', line)
        print('%s %d' % (m.group(1), p))


def vector(size, val=0):
    vec = [val for i in range(size)]
    return vec


def matrix(rowNum, colNum, val=0):
    mat = []
    for i in range(rowNum):
        collumn = [val for j in range(colNum)]
        mat.append(collumn)
    return mat


def dmain():
    setrecursionlimit(100000000)
    threading.stack_size(40960000)
    thread = threading.Thread(target=main)
    thread.start()


if __name__ == '__main__':
    # main()
    dmain()