One day, Bessie was gazing off into the distance at the beautiful Wisconsin mountains when she wondered to herself: which is the widest one?
She decided to take $N$ ($1 \le N \le 10,000$) height measurements $H_{i}$ ($1 \le H_{i} \le 1,000,000,000$) sequentially along the horizon using her new Acme Long Distance Geoaltimeter.
A mountain is defined to be a consecutive sequence of $H_{i}$ values
which increases (or stays the same) and then decreases (or stays
the same), e.g., 2, 3, 3, 5, 4, 4, 1. It is possible for a mountain
on the edge of her field of vision only to increase or only to
decrease in height, as well.
The width of a mountain is the number of measurements it encompasses. Help Bessie identify the widest mountain.
Here's a simple example of a typical horizon:
******* *
********* ***
********** *****
*********** ********* *
* ***************** *********** *** *
** ******************* ************* * * ******* *
**********************************************************************
?ddsssuussuussssssddddssddssssuuuuuuuuddddddssududssssuuudduddsssssuds
3211112333677777776543332111112344456765432111212111112343232111111211
aaaaa cccccccccccccccccccc eeeeeee ggggggggg
bbbbbbbbbbbbbbbbbbbbbbbbbbbb ddddd ffffffffff hhhhhhhhhThe mountains are marked 'a', 'b', etc. Obviously, mountain b is widest with width 28.
Hint: Sometimes it's easiest to find a mountain's width by knowing where its highest parts are.
Input
- Line 1: A single integer: $N$
- Lines $2..N+1$: Line $i+1$ contains a single integer: $H_{i}$
Output
- Line 1: A single line with a single integer that is the width of the widest mountain.
Examples
Input 1
7 3 2 3 5 4 1 6
Output 1
5
The height measurements are 3, 2, 3, 5, 4, 1, 6.
The widest mountain consists of the measurements 2, 3, 5, 4, 1. Other mountains include 3, 2 and 1, 6
Problem credits: Jeffrey Wang, 2009