For a given sequence A = {a0, a1, ... , an-1}, find the length of the longest increasing subsequnece (LIS) in A.
An increasing subsequence of A is defined by a subsequence {ai0, ai1, ... , aik} where 0 ≤ i0 < i1 < ... < ik < n and ai0 < ai1 < ... < aik.
Input
n
a0
a1
:
an-1
In the first line, an integer n is given. In the next n lines, elements of A are given.
Output
The length of the longest increasing subsequence of A.
Constraints
- 1 ≤ n ≤ 100000
- 0 ≤ ai ≤ 109
Sample Input 1
5
5
1
3
2
4
Sample Output 1
3
Sample Input 2
3
1
1
1
Sample Output 2
1