Determine if an N-sided polygon (not necessarily convex) with sides of length L_1, L_2, ..., L_N can be drawn in a two-dimensional plane.

You can use the following theorem:

Theorem: an N-sided polygon satisfying the condition can be drawn if and only if the longest side is strictly shorter than the sum of the lengths of the other N-1 sides.

Constraints

* All values in input are integers.
* 3 \leq N \leq 10
* 1 \leq L_i \leq 100

Input

Input is given from Standard Input in the following format:


N
L_1 L_2 ... L_N


Output

If an N-sided polygon satisfying the condition can be drawn, print `Yes`; otherwise, print `No`.

Examples

Input

4
3 8 5 1


Output

Yes


Input

4
3 8 4 1


Output

No


Input

10
1 8 10 5 8 12 34 100 11 3


Output

No
from fractions import gcd
from math import factorial, ceil, sqrt, atan2, log, pi, e, asin,acos, cos, sin, floor, atan
from itertools import *
from fractions import Fraction
import string
import copy
import random
import bisect
from decimal import *
from collections import deque
from sys import *
digs = string.digits + string.ascii_letters

def id_generator(size=20, chars=string.digits):
    return ''.join(random.choice(chars) for _ in range(size))
 
def mp():
    return map(int,str(raw_input()).strip().split())

clear=stdout.flush()

n=input()
l=list(mp())
l.sort()
z=sum(l[:n-1])
if z>l[-1]:
	print "Yes"
else:
	print "No"