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

Example Output

4 1 1 0 0