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