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

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`