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 <algorithm>
#include <bits/stdc++.h>
#include <cfloat>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <functional>
#include <iostream>
#include <map>
#include <math.h>
#include <memory>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <stdio.h>
#include <string>
#include <utility>
#include <vector>

#define REP(i, n) for(int i = 0; i != n; ++i)
#define REPR(i, n) for(int i = n - 1; i != -1; --i)
#define FOR(i, a, b) for(int i = a; i != b; ++i)
#define RBF(i, n) for(auto &i : n)
#define ABS(n) (n < 0 ? -n : n)
#define MIN(a, b) (a < b ? a : b)
#define MAX(a, b) (a > b ? a : b)
#define IN(n) (cin >> n)
#define OUT(n) (cout << n << "\n")
#define INF 1e9
#define ALL(v) (v).begin(), (v).end()
#define RALL(v) (v).rbegin(), (v).rend()
#define PB push_back
#define MP make_pair
#define EACH(i,c) for(typeof((c).begin()) i=(c).begin(); i!=(c).end(); ++i)
#define EXIST(s,e) ((s).find(e)!=(s).end())
#define SORT(c) sort((c).begin(),(c).end())

//debug
#define dump(x)  cerr << #x << " = " << (x) << endl;
#define debug(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ")" << " " << __FILE__ << endl;

using namespace std;
using ll = long long;

inline int toInt(string s) {int v; istringstream sin(s);sin>>v;return v;}
template<class T> inline string toString(T x) {ostringstream sout;sout<<x;return sout.str();}


void Main() {
  int N;
  IN(N);
  int mx=0;
  int sum=0;
  vector<int> X(N);
  REP(i,N){
    IN(X[i]);
    if(X[i] > mx) mx=X[i];
    sum += X[i];
  }
  if(sum-mx > mx) OUT("Yes");
  else OUT("No");
}

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  std::cout << std::fixed << std::setprecision(15);
  Main();

  return 0;
}