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