Longest Increasing Subsequence

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.

Constraints

• 1 ≤ n ≤ 100000
• 0 ≤ ai ≤ 109

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.

Examples

Input

5 5 1 3 2 4

Output

3

Input

3 1 1 1

Output

1

inputFormat

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.

outputFormat

Output

The length of the longest increasing subsequence of A.

Examples

Input

5 5 1 3 2 4

Output

3

Input

3 1 1 1

Output

1

样例

5
5
1
3
2
4

3