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B - Polygon

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.

4
3 8 5 1

Yes

Since $8 < 9 = 3 + 5 + 1$, it follows from the theorem that such a polygon can be drawn on a plane.

4
3 8 4 1

No

Since $8 \geq 8 = 3 + 4 + 1$, it follows from the theorem that such a polygon cannot be drawn on a plane.

10
1 8 10 5 8 12 34 100 11 3

No