Problem:
Score : 200 points

Problem Statement

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.

Sample Input 1

4
3 8 5 1

Sample Output 1

Yes

Since 8 < 9 = 3 + 5 + 1, it follows from the theorem that such a polygon can be drawn on a plane.

Sample Input 2

4
3 8 4 1

Sample Output 2

No

Since 8 \geq 8 = 3 + 4 + 1, it follows from the theorem that such a polygon cannot be drawn on a plane.

Sample Input 3

10
1 8 10 5 8 12 34 100 11 3

Sample Output 3

No

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
#define itn int
#define nibu(K,x) binary_search(K.begin(),K.end(),x)
#define rep(i,n) for(int i=0;i<n;i++)
#define all(x) x.begin(),x.end()
#define sz(x) x.size()
#define pb push_back
#define mp make_pair
#define F first
#define S second
#define out(x) cout<<x<<endl
#define put(x) out(x)
#define in(x) cin>>x
#define maxx(a,b,c) max(a,max(b,c))
#define minn(a,b,c) min(a,min(b,c))
using ll = long long;
using vl = vector<ll>;
using vs = vector<string>;
const double pi = 3.14159265358979;
const ll mod = 1000000007;

int main() {
int N;
  in(N);
  vl A(N);
  rep(i,N) in(A[i]);
  sort(all(A));
  int m  = A[N-1];
  int wa = 0;
  rep(i,N) wa += A[i];
  if(m<wa-m) out("Yes");
  else out("No");
}