LPIS - Longest Perfect Increasing Subsequence


Dhrubo has a sequence of N integers. He is trying to find the longest perfect increasing subsequence of that sequence. But he is not very expert in finding longest perfect increasing subsequences. So he needs your help.

A subsequence is a sequence that can be derived by another sequence by deleting elements without changing the order of the remaining elements. An increasing subsequence of a sequence is a subsequence where the elements are sorted in increasing order.

Difference between an increasing subsequence and a perfect increasing subsequence is that in a perfect increasing subsequence the difference between any two consecutive elements is always 1.

For example, let’s consider a sequence S= {5, 2, 6, 3, 7, 8, 4}

{5, 3, 4} is subsequence of sequence S but not an increasing subsequence.

{5, 7, 8} is an increasing subsequence of sequence S, but not a perfect increasing subsequence.

But {5, 6, 7, 8} is perfect increasing subsequence as the difference between any two consecutive elements is exactly 1.

Note that, a single element will always be perfect increasing subsequence. So {5}, {2}, {7} are also perfect increasing subsequence of S.

Input

First line of the input contains an integer N (1 <= N <= 105) denoting the length of the sequence.

Next line contains N integers separated by space which is the sequence. These integers will be greater than 0 and will not be greater than 106.

Output

A single integer in a line denoting the length of the longest perfect increasing subsequence.

Example

Input #1:
9
5 1 5 6 2 3 8 7 4

Output #1:
4
Input #2:
8
2 2 1 3 5 4 5 6

Output #2:
5

(set by : Nashir Ahmed)


hide comments
siddharth__: 2015-12-26 03:58:30

It took almost 1 hr to think for an o(n) solution after getting TLE....
FEELING AWESOME #My 50th AC <3 :)

Siddharth Singh: 2015-12-24 06:56:24

knight_1s :
for the first input
ans is { 1,2,3,4 }
they have asked for largest subsequence length with diff between consecutive terms = 1 .

knight_1s: 2015-12-23 21:56:57

why is the first sequence of 4 length,not 7?

Siddharth Singh: 2015-12-23 09:38:49

Truly Awesome Problem
Tried DP O(n^2) Solution got TLE As Expected (Same As Supratim)
Tried DP O(n Log n) Solution Got WA bcox i couldnt solve correctly the cases as i m a beginner in DP
Tried a Non DP O(n) Solution Got AC in .13s
#15th In Ranklist <3

naruto09: 2015-12-22 16:52:21

no need of DP..O(n) solution is possible

Md. Najim Ahmed: 2015-12-18 06:31:01

@Supratim Watch out for overall time complexity of your code ...

Supratim: 2015-12-18 06:27:19

DP approach is giving TLE :(


Added by:Md. Najim Ahmed
Date:2015-12-10
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64 GOSU JS-MONKEY