Time Limit: 2 seconds
Memory Limit: 256 megabytes
Squirrel Liss is interested in sequences. She also has preferences of integers. She thinks n integers a1, a2, ..., an are good.
Now she is interested in good sequences. A sequence x1, x2, ..., xk is called good if it satisfies the following three conditions:
Find the length of the longest good sequence.
The input consists of two lines. The first line contains a single integer n (1 ≤ n ≤ 105) — the number of good integers. The second line contains a single-space separated list of good integers a1, a2, ..., an in strictly increasing order (1 ≤ ai ≤ 105; ai < ai + 1).
In the first example, the following sequences are examples of good sequences: [2; 4; 6; 9], [2; 4; 6], [3; 9], . The length of the longest good sequence is 4.