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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
#define watch(x) cout << (#x) << " is " << (x) << '\n'
#define rep(i,a,n) for (int i=a;i<n;i++)
#define per(i,a,n) for (int i=n-1;i>=a;i--)
#define pb push_back
#define mp make_pair
#define all(x) (x).begin(),(x).end()
#define fi first
#define se second
#define sz(x) ((int)(x).size())
typedef long long ll;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef pair<int, int> pi;
typedef pair<ll, ll> pll;
typedef double db;
ll gcd(ll a, ll b) { return b?gcd(b,a%b):a; }
//head

void solve(){
    int n;
    cin >> n;
    vector<int> l(n);
    ll s = 0;
    for (int i = 0; i < n; i++){
        cin >> l[i];
        s += l[i];
    }
    sort(all(l));
    string ans;
    if (l[n-1] < s-l[n-1]) ans = "Yes\n";
    else ans = "No\n";
    cout << ans; 
}

int main(void){ 
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);

    //int t; cin >> t; while (t--)
        solve();
}