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>

#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define repr(i, n) for(int i = (int)(n); i >= 0; i--)
#define repm(i, m, n) for(int i = (int)(m); i < (int)(n); i++)
#define repmr(i, m, n) for(int i = (int)(n); i >= (int)(m); i--)
#define all(x) (x).begin(),(x).end()
#define inf 2e9
#define MOD 1000000007

using namespace std;
typedef long long int lli;
typedef long long ll;

int main() {
    int n;
    cin >> n;
    vector<int> l(n);
    rep(i,n) cin >> l[i];

    int max_len = 0;
    int sum = 0;
    rep(i,n){
        max_len = max(l[i],max_len);
        sum += l[i];
    }

    cout << (max_len < sum-max_len ? "Yes":"No") << endl;
}