10536: ABC117 —— B - Polygon
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Description
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.
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
Input is given from Standard Input in the following format:
```
$N$
$L_1$ $L_2$ $...$ $L_N$
```
```
$N$
$L_1$ $L_2$ $...$ $L_N$
```
Output
If an $N$-sided polygon satisfying the condition can be drawn, print `Yes`; otherwise, print `No`.
Constraints
- All values in input are integers.
- $3 \leq N \leq 10$
- $1 \leq L_i \leq 100$
- $3 \leq N \leq 10$
- $1 \leq L_i \leq 100$
Sample 1 Input
4
3 8 5 1
Sample 1 Output
Yes
Since 8<9=3+5+1, it follows from the theorem that such a polygon can be drawn on a plane.
Sample 2 Input
4
3 8 4 1
Sample 2 Output
No
Since 8≥8=3+4+1, it follows from the theorem that such a polygon cannot be drawn on a plane.
Sample 3 Input
10
1 8 10 5 8 12 34 100 11 3
Sample 3 Output
No