Sequence Equation

Given a sequence of n integers, p(1), p(2), ..., p(n) where each element is distinct and satisfies . For each x where , find any integer y such that p(p(y)) and print the value of y on a new line.

For example, assume the sequence p = [5, 2, 1, 3, 4]. Each value of x between 1 and 5, the length of the sequence, is analyzed as follows:

1. x = 1 p[3], p[4] = 3, so p[p[4]] = 1
2. x = 2 p[2], p[2] = 2, so p[p[2]] = 2
3. x = 3 p[3], p[5] = 4, so p[p[5]] = 3
4. x = 4 p[5], p[1] = 5, so p[p[1]] = 4
5. x = 5 p[1], p[3] = 1, so p[p[3]] = 5

The values for yare [4, 2, 5, 1, 3].

Function Description

Complete the permutationEquation function in the editor below. It should return an array of integers that represent the values of y.

permutationEquation has the following parameter(s):

• p: an array of integers

Input Format

The first line contains an integer n, the number of elements in the sequence.
The second line contains n space-separated integers p[i] where .

Constraints

• )
• ), where ).
• Each element in the sequence is distinct.

Output Format

For each x from 1 to n, print an integer denoting any valid y satisfying the equation p(p(y)) on a new line.

Sample Input 0

1
2

3
2 3 1

Sample Output 0

1
2
3

2
3
1

Explanation 0

Given the values of p(1) = 2, p(2) = 3, and p(3) = 1, we calculate and print the following values for each x from 1 to n:

1. x = 1 p(3) = p(p(2)) = p(p(y)), so we print the value of y = 2 on a new line.
2. x = 2 p(1) = p(p(3)) = p(p(y)), so we print the value of y = 3 on a new line.
3. x = 3 p(2) = p(p(1)) = p(p(y)), so we print the value of y = 1 on a new line.

Sample Input 1

1
2

5
4 3 5 1 2

Sample Output 1

1
2
3
4
5

1
3
5
4
2

Solution

1
2
3
4

function permutationEquation(p) {
  const findCurrentIndex = arr => arr.map((v, i) => p.findIndex(innerV => innerV === v) + 1);
  return findCurrentIndex(findCurrentIndex(new Array(p.length).fill(0).map((v, i) => i + 1)));
}