Elite Squad Selection

In the Kingdom of Lanqiao, a team of warriors is arranged in a fixed order. The team consists of \(n\) warriors, each with a strength value \(a_1, a_2, \dots, a_n\).

The king has issued an order to select an elite squad from the team. The squad must satisfy the following conditions:

1. The squad members must be chosen while preserving the original order of the warriors.
2. The strength of the first and the last warrior of the squad must be strictly greater than the strength of every other warrior in the squad.

The strength of a squad is directly proportional to the number of its members; that is, the more members the squad has, the stronger it is. Help the king determine the maximum possible number of members in an elite squad.

Note: A single warrior is always considered a valid squad.

inputFormat

The input consists of two lines:

• The first line contains an integer \(n\) \( (1 \leq n \leq 10^3)\) representing the number of warriors.
• The second line contains \(n\) space-separated integers \(a_1, a_2, \dots, a_n\), each representing the strength of a warrior.

outputFormat

Output a single integer, which is the maximum number of members in an elite squad that can be formed under the given conditions.

sample

3
1 2 3

2