Problem Statement

There is an empty sequence X and an empty stack S. Also, you are given an integer sequence $A=(a_1,\ldots,a_N)$ of length N.
For each $i=1,\ldots,N$ in this order, Takahashi will do one of the following operations:

• Move the integer a_i onto the top of S.
• Discard the integer a_i from A.

Additionally, Takahashi may do the following operation whenever S is not empty:

• Move the integer at the top of S to the tail of X.

The score of the final X is defined as follows.

• If X is non-decreasing, i.e. if $x_i \leq x_{i+1}$ holds for all integer $i(1 \leq i \lt |X|)$, where $X=(x_1,\ldots,x_{|X|})$, then the score is |X| (where |X| denotes the number of terms in X).
• If X is not non-decreasing, then the score is 0.

Find the maximum possible score.

Input

Input is given from Standard Input in the following format:
N
$a_1 \ldots a_N$

Output

Print the answer.

Constraints

• $1 \leq N \leq 50$
• $1 \leq a_i \leq 50$
• All values in input are integers.

Sample Input 1

7
1 2 3 4 1 2 3

Sample Output 1

5

The following operations make the final X equal (1,1,2,3,4), for a score of 5.

• Move a_1=1 onto the top of S.
• Move 1 at the top of S to the tail of X.
• Move a_2=2 onto the top of S.
• Discard a_3=3.
• Move a_4=4 onto the top of S.
• Move a_5=1 onto the top of S.
• Move 1 at the top of S to the tail of X.
• Move a_6=2 onto the top of S.
• Move 2 at the top of S to the tail of X.
• Move a_7=3 onto the top of S.
• Move 3 at the top of S to the tail of X.
• Move 4 at the top of S to the tail of X.

We cannot make the score 6 or greater, so the maximum possible score is 5.

Sample Input 2

10
1 1 1 1 1 1 1 1 1 1

Sample Output 2

10

见题面 Input 部分

见题面 Output 部分