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>
#include <boost/multiprecision/cpp_int.hpp>
using namespace std;
namespace mp = boost::multiprecision;
long int MOD = (int)1e9 + 7;

template<typename T> istream& operator>>(istream &s, vector<T> &v) {
    for (T &t : v) s >> t;
    return s;
}
template<typename T> ostream& operator<<(ostream &s, const vector<T> &v) {
    for (const T &t : v) s << t << endl;
    return s;
}
template<typename T> T min(const vector<T>& v) {return *min_element(v.begin(), v.end());}
template<typename T> T max(const vector<T>& v) {return *max_element(v.begin(), v.end());}
template<typename T> int min_element(vector<T>& v) {return min_element(v.begin(), v.end()) - v.begin();}
template<typename T> int max_element(vector<T>& v) {return max_element(v.begin(), v.end()) - v.begin();}
template<typename T> void sort(vector<T>& v) {sort(v.begin(), v.end());}
template<typename T> void greatersort(vector<T>& v) {sort(v.begin(), v.end(), greater<>());}
template<typename T, typename Function> void sort(vector<T>& v, Function func) {sort(v.begin(), v.end(), func);}
template<typename T> void rsort(vector<T>& v) {sort(v.rbegin(), v.rend());}
template<typename T> void reverse(vector<T>& v) {reverse(v.begin(), v.end());}
template<typename T> void unique(vector<T>& v) {v.erase(unique(v.begin(), v.end()), v.end());}
template<typename T> void nth_element(vector<T>& v, int n) {nth_element(v.begin(), v.begin() + n, v.end());}
template<typename T> bool next_permutation(vector<T>& v) {return next_permutation(v.begin(), v.end());}
template<typename T> int find(vector<T>& v, T t) {return find(v.begin(), v.end(), t) - v.begin();}
template<typename T> int in(vector<T> v, T t) {return find(v, t) != int(v.size());}
template<typename T> int lower_bound(vector<T>& v, T t) {return lower_bound(v.begin(), v.end(), t) - v.begin();}
template<typename T> int upper_bound(vector<T>& v, T t) {return upper_bound(v.begin(), v.end(), t) - v.begin();}
template<typename T> T accumulate(const vector<T>& v, function<T(T, T)> func = plus<T>()) {return accumulate(v.begin(), v.end(), T(), func);}
template<typename T> void adjacent_difference(vector<T>& v) {adjacent_difference(v.begin(), v.end(), v.begin());}
template<typename T> void adjacent_difference(vector<T>& v, vector<T>& u) {adjacent_difference(v.begin(), v.end(), u.begin());}
template<typename T> vector<T> partial_sum(const vector<T>& v) {
    vector<T> u(v.size());
    partial_sum(v.begin(), v.end(), u.begin());
    return u;
}\
template<typename T> T inner_product(vector<T>& v, vector<T>& u) {return inner_product(v.begin(), v.end(), u.begin(), T(0));}
template<typename T> int count(const vector<T>& v, T t) {return count(v.begin(), v.end(), t);}
template<typename T, typename Function> int count_if(const vector<T>& v, Function func) {return count_if(v.begin(), v.end(), func);}
template<typename T, typename Function> void remove_if(vector<T>& v, Function func) {v.erase(remove_if(v.begin(), v.end(), func), v.end());}
template<typename T, typename Function> bool all_of(vector<T> v, Function func) {return all_of(v.begin(), v.end(), func);}
template<typename T, typename Function> bool any_of(vector<T> v, Function func) {return any_of(v.begin(), v.end(), func);}
template<typename T, typename Function> bool none_of(vector<T> v, Function func) {return none_of(v.begin(), v.end(), func);}
template<typename T> vector<T> subvector(vector<T>& v, int a, int b) {return vector<T>(v.begin() + a, v.begin() + b);}
template<typename T> int kinds(const vector<T>& v) {return set<T>(v.begin(), v.end()).size();}
template<typename T> map<T, int> count_kinds(const vector<T>& v) {
    map<T, int> res;
    for (const auto& i : v) ++res[i];
    return res;
}
template<typename T> void iota(vector<T>& v, T t = 0) {iota(v.begin(), v.end(), t);}
template<typename T> bool is_sorted(const vector<T>& v) {return is_sorted(v.begin(), v.end());}
int plusVector(vector<int>& v, int n) {int r = 0; for (int i = 0; i < n; ++i) {r += v[i];} return r;}
void yesno(bool b) {if (b) {cout << "yes" << endl;} else {cout << "no" << endl;}}
void YesNo(bool b) {if (b) {cout << "Yes" << endl;} else {cout << "No" << endl;}}
void YESNO(bool b) {if (b) {cout << "YES" << endl;} else {cout << "NO" << endl;}}
long addMOD(long a, long b) {return (a + b) % MOD;}
long subMOD(long a, long b) {return (a + MOD - b) % MOD;}
long mulMOD(long a, long b) {return ((a % MOD) * (b % MOD)) % MOD;}
long long invMOD(long long a, long long m) {long long b = m, u = 1, v = 0;while (b) {long long t = a / b;a -= t * b; swap(a, b);u -= t * v; swap(u, v);}u %= m;if (u < 0) u += m;return u;}
double PI = 3.1415926535897932384626433832795;

int main() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    int N;
    cin >> N;
    vector<int> L(N);
    cin >> L;
    if (max(L) < accumulate(L) - max(L)) {
        cout << "Yes" << endl;
    } else {
        cout << "No" << endl;
    }
}