**Time limit:**1.00 s**Memory limit:**512 MB

You are playing a game consisting of n planets. Each planet has a teleporter to another planet (or the planet itself).

You start on a planet and then travel through teleporters until you reach a planet that you have already visited before.

Your task is to calculate for each planet the number of teleportations there would be if you started on that planet.

# Input

The first input line has an integer n: the number of planets. The planets are numbered 1,2,\dots,n.

The second line has n integers t_1,t_2,\dots,t_n: for each planet, the destination of the teleporter. It is possible that t_i=i.

# Output

Print n integers according to the problem statement.

# Constraints

- 1 \le n \le 2 \cdot 10^5
- 1 \le t_i \le n

# Example

Input:

5 2 4 3 1 4

Output:

3 3 1 3 4