The Widest Mountain

Bessie was gazing into the distance at a beautiful mountain range along the horizon when she wondered to herself: which mountain is the widest?

She took $N$ ($1 \le N \le 100000$) equally-spaced height measurements in order along the horizon. Let $H_i$ ($1 \le H_i \le 10^9$) be the $i$-th measurement.

A mountain is a consecutive sequence of measurements whose values first increase (or stay the same) and then decrease (or stay the same); for example, $2, 3, 3, 5, 4, 4, 1$ is one mountain. A mountain at the edge of the horizon may only increase or only decrease.

The width of a mountain is the number of measurements it contains. Find the width of the widest mountain.

Here is one example of a horizon:

           *******                   *
          *********                 ***
          **********               *****
          ***********           *********               *
*      *****************       ***********             *** *
**    *******************     *************   * *     *******      *
**********************************************************************
3211112333677777776543332111112344456765432111212111112343232111111211
aaaaaa                   ccccccccccccccccccccc eeeeeee    ggggggggg
  bbbbbbbbbbbbbbbbbbbbbbbbbbbb             ddddd ffffffffff  hhhhhhhhh

The mountains are labeled 'a', 'b', and so on. Here mountain b is the widest, with width $28$. The leftmost mountain a has width $6$ for the purposes of this problem.

• Line 1: a single integer $N$.
• Lines 2 to $N+1$: line $i+1$ contains a single integer $H_i$.

• Line 1: a single integer, the width of the widest mountain.

Two neighboring mountains share the valley between them: the measurement at the bottom of a valley belongs to both the mountain on its left and the mountain on its right, so it is counted in the width of each.