Contest Duration: - (local time) (100 minutes) Back to Home
B - Polygon /

Time Limit: 2 sec / Memory Limit: 1024 MB

問題文

2 次元平面上に辺の長さがそれぞれ L_1, L_2, ..., L_NN 角形(凸多角形でなくてもよい)が描けるかを判定してください。

ここで、次の定理を利用しても構いません。

制約

• 入力は全て整数である。
• 3 \leq N \leq 10
• 1 \leq L_i \leq 100

入力

N
L_1 L_2 ... L_N


入力例 1

4
3 8 5 1


出力例 1

Yes


8 < 9 = 3 + 5 + 1 なので、定理より 2 次元平面上に条件を満たす N 角形が描けます。

入力例 2

4
3 8 4 1


出力例 2

No


8 \geq 8 = 3 + 4 + 1 なので、定理より 2 次元平面上に条件を満たす N 角形は描けません。

入力例 3

10
1 8 10 5 8 12 34 100 11 3


出力例 3

No


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