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Codeforces Round 198 (Div. 2) |
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Finished |

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data structures

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*1500

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D. Bubble Sort Graph

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputIahub recently has learned Bubble Sort, an algorithm that is used to sort a permutation with *n* elements *a*_{1}, *a*_{2}, ..., *a*_{n} in ascending order. He is bored of this so simple algorithm, so he invents his own graph. The graph (let's call it *G*) initially has *n* vertices and 0 edges. During Bubble Sort execution, edges appear as described in the following algorithm (pseudocode).

procedure bubbleSortGraph()

build a graph G with n vertices and 0 edges

repeat

swapped = false

for i = 1 to n - 1 inclusive do:

if a[i] > a[i + 1] then

add an undirected edge in G between a[i] and a[i + 1]

swap( a[i], a[i + 1] )

swapped = true

end if

end for

until not swapped

/* repeat the algorithm as long as swapped value is true. */

end procedure

For a graph, an independent set is a set of vertices in a graph, no two of which are adjacent (so there are no edges between vertices of an independent set). A maximum independent set is an independent set which has maximum cardinality. Given the permutation, find the size of the maximum independent set of graph *G*, if we use such permutation as the premutation *a* in procedure bubbleSortGraph.

Input

The first line of the input contains an integer *n* (2 ≤ *n* ≤ 10^{5}). The next line contains *n* distinct integers *a*_{1}, *a*_{2}, ..., *a*_{n} (1 ≤ *a*_{i} ≤ *n*).

Output

Output a single integer — the answer to the problem.

Examples

Input

3

3 1 2

Output

2

Note

Consider the first example. Bubble sort swaps elements 3 and 1. We add edge (1, 3). Permutation is now [1, 3, 2]. Then bubble sort swaps elements 3 and 2. We add edge (2, 3). Permutation is now sorted. We have a graph with 3 vertices and 2 edges (1, 3) and (2, 3). Its maximal independent set is [1, 2].

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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