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 rep(i, n) for (int i = (int)(0); i < (int)(n); ++i)
#define reps(i, n) for (int i = (int)(1); i <= (int)(n); ++i)
#define rrep(i, n) for (int i = ((int)(n)-1); i >= 0; i--)
#define rreps(i, n) for (int i = ((int)(n)); i > 0; i--)
#define irep(i, m, n) for (int i = (int)(m); i < (int)(n); ++i)
#define ireps(i, m, n) for (int i = (int)(m); i <= (int)(n); ++i)
#define FOR(e, c) for (auto &e : c)
#define SORT(v, n) sort(v, v + n);
#define vsort(v) sort(v.begin(), v.end());
#define rvisort(v) sort(v.begin(), v.end(), greater<int>());
#define all(v) v.begin(), v.end()
#define mp(n, m) make_pair(n, m);
#define cout(d) cout<<d<<endl;
#define coutd(d) cout<<std::setprecision(10)<<d<<endl;
#define cinline(n) getline(cin,n);

using ll = long long;
using vi = vector<int>;
using vvi = vector<vi>;
using vll = vector<ll>;
using vvll = vector<vll>;
using pii = pair<int, int>;
using vpii = vector<pii>;
using vs = vector<string>;
using vd = vector<double>;
using ul = unsigned long;

template<class T, class C> void chmax(T& a, C b){ a>b?:a=b; }
template<class T, class C> void chmin(T& a, C b){ a<b?:a=b; }

const int mod=1e9+7;

struct mint {
  ll x;
  mint(ll x=0):x(x%mod){}
  mint& operator+=(const mint a) {
    if ((x += a.x) >= mod) x -= mod;
    return *this;
  }
  mint& operator-=(const mint a) {
    if ((x += mod-a.x) >= mod) x -= mod;
    return *this;
  }
  mint& operator*=(const mint a) {
    (x *= a.x) %= mod;
    return *this;
  }
  mint operator+(const mint a) const {
    mint res(*this);
    return res+=a;
  }
  mint operator-(const mint a) const {
    mint res(*this);
    return res-=a;
  }
  mint operator*(const mint a) const {
    mint res(*this);
    return res*=a;
  }
};

mint c[4005][4005];
void init() {
  c[0][0] = 1;
  for (int i = 0; i <= 4000; i++) {
    for (int j = 0; j <= i; j++) {
      c[i+1][j] += c[i][j];
      c[i+1][j+1] += c[i][j];
    }
  }
}
mint comb(int n, int k) {
  return c[n][k];
}

bool IsPrime(int num)
{
    if (num < 2) return false;
    else if (num == 2) return true;
    else if (num % 2 == 0) return false;

    double sqrtNum = sqrt(num);
    for (int i = 3; i <= sqrtNum; i += 2)
    {
        if (num % i == 0)
        {
            return false;
        }
    }

    return true;
}

map<ll, ll> primeFact(ll n) {
  map<ll, ll> res;
  for (ll i = 2; i * i <= n; i++) {
    while (n % i == 0) {
      res[i]++;
      n /= i;
    }
  }
  if (n != 1) res[n]++;
  return res;
}

void printv(vi& v){
  rep(i,v.size()) cout << v[i] << " ";
  cout << endl;
}
void printv(vll& v){
  rep(i,v.size()) cout << v[i] << " ";
  cout << endl;
}
int vtotal(vi& v){
  int total=0;
  rep(i,v.size()) total+=v[i];
  return total;
}

int main()
{
  //init(); // mint初期化
  cin.tie( 0 );
  ios::sync_with_stdio( false );

  int n;cin>>n;
  vi l(n);
  rep(i,n)cin>>l[i];
  rvisort(l);
  int max=l[0];
  int other=vtotal(l)-max;
  string ans="No";
  if(max<other)ans="Yes";
  
  cout(ans);

  return 0;
}