Given the structure of a company, your task is to calculate for each employee the number of their subordinates.

Input

The first input line has an integer $n$: the number of employees. The employees are numbered $1,2,\dots,n$, and employee $1$ is the general director of the company.

After this, there are $n-1$ integers: for each employee $2,3,\dots,n$ their direct boss in the company.

Output

Print $n$ integers: for each employee $1,2,\dots,n$ the number of their subordinates.

Constraints

• $1 \le n \le 2 \cdot 10^5$

Example

Input:

5
1 1 2 3

Output:

4 1 1 0 0