
Score : 200 points
Problem StatementDetermine 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
InputInput is given from Standard Input in the following format:
N
L_1 L_2 ... L_N
OutputIf an N-sided polygon satisfying the condition can be drawn, print Yes; otherwise, print No.
Sample Input 14
3 8 5 1
Sample Output 1Yes
Since 8 < 9 = 3 + 5 + 1, it follows from the theorem that such a polygon can be drawn on a plane.
Sample Input 24
3 8 4 1
Sample Output 2No
Since 8 \geq 8 = 3 + 4 + 1, it follows from the theorem that such a polygon cannot be drawn on a plane.
Sample Input 310
1 8 10 5 8 12 34 100 11 3
Sample Output 3No
