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AVAILABLE LESSONS:

Lesson 1

Iterations

Lesson 2

Arrays

Lesson 3

Time Complexity

Lesson 4

Counting Elements

Lesson 5

Prefix Sums

Lesson 6

Sorting

Lesson 7

Stacks and Queues

Lesson 8

Leader

Lesson 9

Maximum slice problem

Lesson 10

Prime and composite numbers

Lesson 11

Sieve of Eratosthenes

Lesson 12

Euclidean algorithm

Lesson 13

Fibonacci numbers

Lesson 14

Binary search algorithm

Lesson 15

Caterpillar method

Lesson 16

Greedy algorithms

Lesson 17

Dynamic programming

Lesson 90

Tasks from Indeed Prime 2015 challenge

Lesson 91

Tasks from Indeed Prime 2016 challenge

Lesson 92

Tasks from Indeed Prime 2016 College Coders challenge

Lesson 99

Future training

Spoken language:

A non-empty array A consisting of N integers is given.

A *peak* is an array element which is larger than its neighbors. More precisely, it is an index P such that 0 < P < N − 1, A[P − 1] < A[P] and A[P] > A[P + 1].

For example, the following array A:

has exactly three peaks: 3, 5, 10.

We want to divide this array into blocks containing the same number of elements. More precisely, we want to choose a number K that will yield the following blocks:

- A[0], A[1], ..., A[K − 1],
- A[K], A[K + 1], ..., A[2K − 1],

...- A[N − K], A[N − K + 1], ..., A[N − 1].

What's more, every block should contain at least one peak. Notice that extreme elements of the blocks (for example A[K − 1] or A[K]) can also be peaks, but only if they have both neighbors (including one in an adjacent blocks).

The goal is to find the maximum number of blocks into which the array A can be divided.

Array A can be divided into blocks as follows:

- one block (1, 2, 3, 4, 3, 4, 1, 2, 3, 4, 6, 2). This block contains three peaks.
- two blocks (1, 2, 3, 4, 3, 4) and (1, 2, 3, 4, 6, 2). Every block has a peak.
- three blocks (1, 2, 3, 4), (3, 4, 1, 2), (3, 4, 6, 2). Every block has a peak. Notice in particular that the first block (1, 2, 3, 4) has a peak at A[3], because A[2] < A[3] > A[4], even though A[4] is in the adjacent block.

However, array A cannot be divided into four blocks, (1, 2, 3), (4, 3, 4), (1, 2, 3) and (4, 6, 2), because the (1, 2, 3) blocks do not contain a peak. Notice in particular that the (4, 3, 4) block contains two peaks: A[3] and A[5].

The maximum number of blocks that array A can be divided into is three.

Write a function:

int solution(int A[], int N);

that, given a non-empty array A consisting of N integers, returns the maximum number of blocks into which A can be divided.

If A cannot be divided into some number of blocks, the function should return 0.

For example, given:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [0..1,000,000,000].

Copyright 2009–2021 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.

A non-empty array A consisting of N integers is given.

A *peak* is an array element which is larger than its neighbors. More precisely, it is an index P such that 0 < P < N − 1, A[P − 1] < A[P] and A[P] > A[P + 1].

For example, the following array A:

has exactly three peaks: 3, 5, 10.

We want to divide this array into blocks containing the same number of elements. More precisely, we want to choose a number K that will yield the following blocks:

- A[0], A[1], ..., A[K − 1],
- A[K], A[K + 1], ..., A[2K − 1],

...- A[N − K], A[N − K + 1], ..., A[N − 1].

What's more, every block should contain at least one peak. Notice that extreme elements of the blocks (for example A[K − 1] or A[K]) can also be peaks, but only if they have both neighbors (including one in an adjacent blocks).

The goal is to find the maximum number of blocks into which the array A can be divided.

Array A can be divided into blocks as follows:

- one block (1, 2, 3, 4, 3, 4, 1, 2, 3, 4, 6, 2). This block contains three peaks.
- two blocks (1, 2, 3, 4, 3, 4) and (1, 2, 3, 4, 6, 2). Every block has a peak.
- three blocks (1, 2, 3, 4), (3, 4, 1, 2), (3, 4, 6, 2). Every block has a peak. Notice in particular that the first block (1, 2, 3, 4) has a peak at A[3], because A[2] < A[3] > A[4], even though A[4] is in the adjacent block.

However, array A cannot be divided into four blocks, (1, 2, 3), (4, 3, 4), (1, 2, 3) and (4, 6, 2), because the (1, 2, 3) blocks do not contain a peak. Notice in particular that the (4, 3, 4) block contains two peaks: A[3] and A[5].

The maximum number of blocks that array A can be divided into is three.

Write a function:

int solution(vector<int> &A);

that, given a non-empty array A consisting of N integers, returns the maximum number of blocks into which A can be divided.

If A cannot be divided into some number of blocks, the function should return 0.

For example, given:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [0..1,000,000,000].

Copyright 2009–2021 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.

A non-empty array A consisting of N integers is given.

A *peak* is an array element which is larger than its neighbors. More precisely, it is an index P such that 0 < P < N − 1, A[P − 1] < A[P] and A[P] > A[P + 1].

For example, the following array A:

has exactly three peaks: 3, 5, 10.

We want to divide this array into blocks containing the same number of elements. More precisely, we want to choose a number K that will yield the following blocks:

- A[0], A[1], ..., A[K − 1],
- A[K], A[K + 1], ..., A[2K − 1],

...- A[N − K], A[N − K + 1], ..., A[N − 1].

What's more, every block should contain at least one peak. Notice that extreme elements of the blocks (for example A[K − 1] or A[K]) can also be peaks, but only if they have both neighbors (including one in an adjacent blocks).

The goal is to find the maximum number of blocks into which the array A can be divided.

Array A can be divided into blocks as follows:

- one block (1, 2, 3, 4, 3, 4, 1, 2, 3, 4, 6, 2). This block contains three peaks.
- two blocks (1, 2, 3, 4, 3, 4) and (1, 2, 3, 4, 6, 2). Every block has a peak.
- three blocks (1, 2, 3, 4), (3, 4, 1, 2), (3, 4, 6, 2). Every block has a peak. Notice in particular that the first block (1, 2, 3, 4) has a peak at A[3], because A[2] < A[3] > A[4], even though A[4] is in the adjacent block.

However, array A cannot be divided into four blocks, (1, 2, 3), (4, 3, 4), (1, 2, 3) and (4, 6, 2), because the (1, 2, 3) blocks do not contain a peak. Notice in particular that the (4, 3, 4) block contains two peaks: A[3] and A[5].

The maximum number of blocks that array A can be divided into is three.

Write a function:

class Solution { public int solution(int[] A); }

that, given a non-empty array A consisting of N integers, returns the maximum number of blocks into which A can be divided.

If A cannot be divided into some number of blocks, the function should return 0.

For example, given:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [0..1,000,000,000].

Copyright 2009–2021 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.

A non-empty array A consisting of N integers is given.

*peak* is an array element which is larger than its neighbors. More precisely, it is an index P such that 0 < P < N − 1, A[P − 1] < A[P] and A[P] > A[P + 1].

For example, the following array A:

has exactly three peaks: 3, 5, 10.

- A[0], A[1], ..., A[K − 1],
- A[K], A[K + 1], ..., A[2K − 1],

...- A[N − K], A[N − K + 1], ..., A[N − 1].

The goal is to find the maximum number of blocks into which the array A can be divided.

Array A can be divided into blocks as follows:

- one block (1, 2, 3, 4, 3, 4, 1, 2, 3, 4, 6, 2). This block contains three peaks.
- two blocks (1, 2, 3, 4, 3, 4) and (1, 2, 3, 4, 6, 2). Every block has a peak.

The maximum number of blocks that array A can be divided into is three.

Write a function:

func Solution(A []int) int

If A cannot be divided into some number of blocks, the function should return 0.

For example, given:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [0..1,000,000,000].

A non-empty array A consisting of N integers is given.

*peak* is an array element which is larger than its neighbors. More precisely, it is an index P such that 0 < P < N − 1, A[P − 1] < A[P] and A[P] > A[P + 1].

For example, the following array A:

has exactly three peaks: 3, 5, 10.

- A[0], A[1], ..., A[K − 1],
- A[K], A[K + 1], ..., A[2K − 1],

...- A[N − K], A[N − K + 1], ..., A[N − 1].

The goal is to find the maximum number of blocks into which the array A can be divided.

Array A can be divided into blocks as follows:

- one block (1, 2, 3, 4, 3, 4, 1, 2, 3, 4, 6, 2). This block contains three peaks.
- two blocks (1, 2, 3, 4, 3, 4) and (1, 2, 3, 4, 6, 2). Every block has a peak.

The maximum number of blocks that array A can be divided into is three.

Write a function:

class Solution { public int solution(int[] A); }

If A cannot be divided into some number of blocks, the function should return 0.

For example, given:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [0..1,000,000,000].

A non-empty array A consisting of N integers is given.

*peak* is an array element which is larger than its neighbors. More precisely, it is an index P such that 0 < P < N − 1, A[P − 1] < A[P] and A[P] > A[P + 1].

For example, the following array A:

has exactly three peaks: 3, 5, 10.

- A[0], A[1], ..., A[K − 1],
- A[K], A[K + 1], ..., A[2K − 1],

...- A[N − K], A[N − K + 1], ..., A[N − 1].

The goal is to find the maximum number of blocks into which the array A can be divided.

Array A can be divided into blocks as follows:

- one block (1, 2, 3, 4, 3, 4, 1, 2, 3, 4, 6, 2). This block contains three peaks.
- two blocks (1, 2, 3, 4, 3, 4) and (1, 2, 3, 4, 6, 2). Every block has a peak.

The maximum number of blocks that array A can be divided into is three.

Write a function:

class Solution { public int solution(int[] A); }

If A cannot be divided into some number of blocks, the function should return 0.

For example, given:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [0..1,000,000,000].

A non-empty array A consisting of N integers is given.

*peak* is an array element which is larger than its neighbors. More precisely, it is an index P such that 0 < P < N − 1, A[P − 1] < A[P] and A[P] > A[P + 1].

For example, the following array A:

has exactly three peaks: 3, 5, 10.

- A[0], A[1], ..., A[K − 1],
- A[K], A[K + 1], ..., A[2K − 1],

...- A[N − K], A[N − K + 1], ..., A[N − 1].

The goal is to find the maximum number of blocks into which the array A can be divided.

Array A can be divided into blocks as follows:

- one block (1, 2, 3, 4, 3, 4, 1, 2, 3, 4, 6, 2). This block contains three peaks.
- two blocks (1, 2, 3, 4, 3, 4) and (1, 2, 3, 4, 6, 2). Every block has a peak.

The maximum number of blocks that array A can be divided into is three.

Write a function:

function solution(A);

If A cannot be divided into some number of blocks, the function should return 0.

For example, given:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [0..1,000,000,000].

A non-empty array A consisting of N integers is given.

*peak* is an array element which is larger than its neighbors. More precisely, it is an index P such that 0 < P < N − 1, A[P − 1] < A[P] and A[P] > A[P + 1].

For example, the following array A:

has exactly three peaks: 3, 5, 10.

- A[0], A[1], ..., A[K − 1],
- A[K], A[K + 1], ..., A[2K − 1],

...- A[N − K], A[N − K + 1], ..., A[N − 1].

The goal is to find the maximum number of blocks into which the array A can be divided.

Array A can be divided into blocks as follows:

- one block (1, 2, 3, 4, 3, 4, 1, 2, 3, 4, 6, 2). This block contains three peaks.
- two blocks (1, 2, 3, 4, 3, 4) and (1, 2, 3, 4, 6, 2). Every block has a peak.

The maximum number of blocks that array A can be divided into is three.

Write a function:

fun solution(A: IntArray): Int

If A cannot be divided into some number of blocks, the function should return 0.

For example, given:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [0..1,000,000,000].

A non-empty array A consisting of N integers is given.

*peak* is an array element which is larger than its neighbors. More precisely, it is an index P such that 0 < P < N − 1, A[P − 1] < A[P] and A[P] > A[P + 1].

For example, the following array A:

has exactly three peaks: 3, 5, 10.

- A[0], A[1], ..., A[K − 1],
- A[K], A[K + 1], ..., A[2K − 1],

...- A[N − K], A[N − K + 1], ..., A[N − 1].

The goal is to find the maximum number of blocks into which the array A can be divided.

Array A can be divided into blocks as follows:

- one block (1, 2, 3, 4, 3, 4, 1, 2, 3, 4, 6, 2). This block contains three peaks.
- two blocks (1, 2, 3, 4, 3, 4) and (1, 2, 3, 4, 6, 2). Every block has a peak.

The maximum number of blocks that array A can be divided into is three.

Write a function:

function solution(A)

If A cannot be divided into some number of blocks, the function should return 0.

For example, given:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [0..1,000,000,000].

Note: All arrays in this task are zero-indexed, unlike the common Lua convention. You can use `#A` to get the length of the array A.

A non-empty array A consisting of N integers is given.

*peak* is an array element which is larger than its neighbors. More precisely, it is an index P such that 0 < P < N − 1, A[P − 1] < A[P] and A[P] > A[P + 1].

For example, the following array A:

has exactly three peaks: 3, 5, 10.

- A[0], A[1], ..., A[K − 1],
- A[K], A[K + 1], ..., A[2K − 1],

...- A[N − K], A[N − K + 1], ..., A[N − 1].

The goal is to find the maximum number of blocks into which the array A can be divided.

Array A can be divided into blocks as follows:

- one block (1, 2, 3, 4, 3, 4, 1, 2, 3, 4, 6, 2). This block contains three peaks.
- two blocks (1, 2, 3, 4, 3, 4) and (1, 2, 3, 4, 6, 2). Every block has a peak.

The maximum number of blocks that array A can be divided into is three.

Write a function:

int solution(NSMutableArray *A);

If A cannot be divided into some number of blocks, the function should return 0.

For example, given:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [0..1,000,000,000].

A non-empty array A consisting of N integers is given.

*peak* is an array element which is larger than its neighbors. More precisely, it is an index P such that 0 < P < N − 1, A[P − 1] < A[P] and A[P] > A[P + 1].

For example, the following array A:

has exactly three peaks: 3, 5, 10.

- A[0], A[1], ..., A[K − 1],
- A[K], A[K + 1], ..., A[2K − 1],

...- A[N − K], A[N − K + 1], ..., A[N − 1].

The goal is to find the maximum number of blocks into which the array A can be divided.

Array A can be divided into blocks as follows:

- one block (1, 2, 3, 4, 3, 4, 1, 2, 3, 4, 6, 2). This block contains three peaks.
- two blocks (1, 2, 3, 4, 3, 4) and (1, 2, 3, 4, 6, 2). Every block has a peak.

The maximum number of blocks that array A can be divided into is three.

Write a function:

function solution(A: array of longint; N: longint): longint;

If A cannot be divided into some number of blocks, the function should return 0.

For example, given:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [0..1,000,000,000].

A non-empty array A consisting of N integers is given.

*peak* is an array element which is larger than its neighbors. More precisely, it is an index P such that 0 < P < N − 1, A[P − 1] < A[P] and A[P] > A[P + 1].

For example, the following array A:

has exactly three peaks: 3, 5, 10.

- A[0], A[1], ..., A[K − 1],
- A[K], A[K + 1], ..., A[2K − 1],

...- A[N − K], A[N − K + 1], ..., A[N − 1].

The goal is to find the maximum number of blocks into which the array A can be divided.

Array A can be divided into blocks as follows:

- one block (1, 2, 3, 4, 3, 4, 1, 2, 3, 4, 6, 2). This block contains three peaks.
- two blocks (1, 2, 3, 4, 3, 4) and (1, 2, 3, 4, 6, 2). Every block has a peak.

The maximum number of blocks that array A can be divided into is three.

Write a function:

function solution($A);

If A cannot be divided into some number of blocks, the function should return 0.

For example, given:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [0..1,000,000,000].

A non-empty array A consisting of N integers is given.

*peak* is an array element which is larger than its neighbors. More precisely, it is an index P such that 0 < P < N − 1, A[P − 1] < A[P] and A[P] > A[P + 1].

For example, the following array A:

has exactly three peaks: 3, 5, 10.

- A[0], A[1], ..., A[K − 1],
- A[K], A[K + 1], ..., A[2K − 1],

...- A[N − K], A[N − K + 1], ..., A[N − 1].

The goal is to find the maximum number of blocks into which the array A can be divided.

Array A can be divided into blocks as follows:

- one block (1, 2, 3, 4, 3, 4, 1, 2, 3, 4, 6, 2). This block contains three peaks.
- two blocks (1, 2, 3, 4, 3, 4) and (1, 2, 3, 4, 6, 2). Every block has a peak.

The maximum number of blocks that array A can be divided into is three.

Write a function:

sub solution { my (@A)=@_; ... }

If A cannot be divided into some number of blocks, the function should return 0.

For example, given:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [0..1,000,000,000].

A non-empty array A consisting of N integers is given.

*peak* is an array element which is larger than its neighbors. More precisely, it is an index P such that 0 < P < N − 1, A[P − 1] < A[P] and A[P] > A[P + 1].

For example, the following array A:

has exactly three peaks: 3, 5, 10.

- A[0], A[1], ..., A[K − 1],
- A[K], A[K + 1], ..., A[2K − 1],

...- A[N − K], A[N − K + 1], ..., A[N − 1].

The goal is to find the maximum number of blocks into which the array A can be divided.

Array A can be divided into blocks as follows:

- one block (1, 2, 3, 4, 3, 4, 1, 2, 3, 4, 6, 2). This block contains three peaks.
- two blocks (1, 2, 3, 4, 3, 4) and (1, 2, 3, 4, 6, 2). Every block has a peak.

The maximum number of blocks that array A can be divided into is three.

Write a function:

def solution(A)

If A cannot be divided into some number of blocks, the function should return 0.

For example, given:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [0..1,000,000,000].

A non-empty array A consisting of N integers is given.

*peak* is an array element which is larger than its neighbors. More precisely, it is an index P such that 0 < P < N − 1, A[P − 1] < A[P] and A[P] > A[P + 1].

For example, the following array A:

has exactly three peaks: 3, 5, 10.

- A[0], A[1], ..., A[K − 1],
- A[K], A[K + 1], ..., A[2K − 1],

...- A[N − K], A[N − K + 1], ..., A[N − 1].

The goal is to find the maximum number of blocks into which the array A can be divided.

Array A can be divided into blocks as follows:

- one block (1, 2, 3, 4, 3, 4, 1, 2, 3, 4, 6, 2). This block contains three peaks.
- two blocks (1, 2, 3, 4, 3, 4) and (1, 2, 3, 4, 6, 2). Every block has a peak.

The maximum number of blocks that array A can be divided into is three.

Write a function:

def solution(a)

If A cannot be divided into some number of blocks, the function should return 0.

For example, given:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [0..1,000,000,000].

A non-empty array A consisting of N integers is given.

*peak* is an array element which is larger than its neighbors. More precisely, it is an index P such that 0 < P < N − 1, A[P − 1] < A[P] and A[P] > A[P + 1].

For example, the following array A:

has exactly three peaks: 3, 5, 10.

- A[0], A[1], ..., A[K − 1],
- A[K], A[K + 1], ..., A[2K − 1],

...- A[N − K], A[N − K + 1], ..., A[N − 1].

The goal is to find the maximum number of blocks into which the array A can be divided.

Array A can be divided into blocks as follows:

- one block (1, 2, 3, 4, 3, 4, 1, 2, 3, 4, 6, 2). This block contains three peaks.
- two blocks (1, 2, 3, 4, 3, 4) and (1, 2, 3, 4, 6, 2). Every block has a peak.

The maximum number of blocks that array A can be divided into is three.

Write a function:

object Solution { def solution(a: Array[Int]): Int }

If A cannot be divided into some number of blocks, the function should return 0.

For example, given:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [0..1,000,000,000].

A non-empty array A consisting of N integers is given.

*peak* is an array element which is larger than its neighbors. More precisely, it is an index P such that 0 < P < N − 1, A[P − 1] < A[P] and A[P] > A[P + 1].

For example, the following array A:

has exactly three peaks: 3, 5, 10.

- A[0], A[1], ..., A[K − 1],
- A[K], A[K + 1], ..., A[2K − 1],

...- A[N − K], A[N − K + 1], ..., A[N − 1].

The goal is to find the maximum number of blocks into which the array A can be divided.

Array A can be divided into blocks as follows:

- one block (1, 2, 3, 4, 3, 4, 1, 2, 3, 4, 6, 2). This block contains three peaks.
- two blocks (1, 2, 3, 4, 3, 4) and (1, 2, 3, 4, 6, 2). Every block has a peak.

The maximum number of blocks that array A can be divided into is three.

Write a function:

public func solution(_ A : inout [Int]) -> Int

If A cannot be divided into some number of blocks, the function should return 0.

For example, given:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [0..1,000,000,000].

A non-empty array A consisting of N integers is given.

*peak* is an array element which is larger than its neighbors. More precisely, it is an index P such that 0 < P < N − 1, A[P − 1] < A[P] and A[P] > A[P + 1].

For example, the following array A:

has exactly three peaks: 3, 5, 10.

- A[0], A[1], ..., A[K − 1],
- A[K], A[K + 1], ..., A[2K − 1],

...- A[N − K], A[N − K + 1], ..., A[N − 1].

The goal is to find the maximum number of blocks into which the array A can be divided.

Array A can be divided into blocks as follows:

- one block (1, 2, 3, 4, 3, 4, 1, 2, 3, 4, 6, 2). This block contains three peaks.
- two blocks (1, 2, 3, 4, 3, 4) and (1, 2, 3, 4, 6, 2). Every block has a peak.

The maximum number of blocks that array A can be divided into is three.

Write a function:

Private Function solution(A As Integer()) As Integer

If A cannot be divided into some number of blocks, the function should return 0.

For example, given:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [0..1,000,000,000].

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