Score : 200 points
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.
Input is given from Standard Input in the following format:
N L_1 L_2 ... L_N
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