Given a list of numbers A output the length of the longest increasing subsequence. An increasing subsequence is defined as a set {i0 , i1 , i2 , i3 , ... , ik} such that 0 <= i0 < i1 < i2 < i3 < ... < ik < N and A[ i0 ] < A[ i1 ] < A[ i2 ] < ... < A[ ik ]. A longest increasing subsequence is a subsequence with the maximum k (length).

i.e. in the list {33 , 11 , 22 , 44}

the subsequence {33 , 44} and {11} are increasing subsequences while {11 , 22 , 44} is the longest increasing subsequence.

Input

First line contain one number N (1 <= N <= 10) the length of the list A.

Second line contains N numbers (1 <= each number <= 20), the numbers in the list A separated by spaces.

Output

One line containing the lenght of the longest increasing subsequence in A.

Example

Input:

5

1 4 2 4 3
Output:
3