Replace Numbers with Their Index in the List

You are given a list of N unique positive numbers ranging from 0 to (N - 1). Write an algorithm to replace the value of each number with its corresponding index value in the list.

Input

• The first line of input consists of an integer size, representing the size of the list (N).
• The next line consists of N space-separated integers, arr[0], arr[1], ..., arr[N-1], representing the given list of numbers.

Output

Print N space-separated integers representing the list obtained by replacing the values of the numbers with their corresponding index values in the list.

Constraints

0 ≤ size ≤ 10^5
0 ≤ arr[i] ≤ 10^5
0 ≤ i < size

Note:

• All the numbers in the list are unique.

Example

Input:

6
5 0 3 2 4 1

Output:

1 5 3 2 4 0

Traveling Salesman Problem

Moche Goldberg is a traveling salesman. He works in N towns. Each day, he sells his products in one of the towns. The towns that are chosen on any two successive days should be different, and a town can be chosen at most count[i] times.

Write an algorithm to determine the number of days when he can sell in the given towns following the above-mentioned rules.

Input

Output

Print an integer representing the maximum number of days starting from which the salesman can work.

Constraints

1 ≤ num ≤ 5 * 10^4
1 ≤ countTown_i ≤ 10^5
∑ countTown_i ≤ 10^5
0 ≤ i < N

Example

Input:

3
7 2 3

Output:

11

Explanation:

The first, second, and third towns are chosen 7, 2, and 3 times, respectively.
The different towns are selected on successive days in this sequence: first, second, third, first, second, first, third, first, third, first, first.
Thus, the maximum number of days the salesman can sell his products is 11.

我们长期稳定承接各大科技公司如TikTok、Google、Amazon等的OA笔试代写服务，确保满分通过。如有需求，请随时联系我们。

We consistently provide professional online assessment services for major tech companies like TikTok, Google, and Amazon, guaranteeing perfect scores. Feel free to contact us if you're interested.