Polygon

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.

Examples

Input

4 3 8 5 1

Output

Yes

Input

4 3 8 4 1

Output

No

Input

10 1 8 10 5 8 12 34 100 11 3

Output

No

inputFormat

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

outputFormat

Output

If an N-sided polygon satisfying the condition can be drawn, print Yes; otherwise, print No.

Examples

Input

4 3 8 5 1

Output

Yes

Input

4 3 8 4 1

Output

No

Input

10 1 8 10 5 8 12 34 100 11 3

Output

No

样例

4
3 8 5 1

Yes