Dice Face Frequencies 1..6

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem

Given $n$ outcomes of a standard die, each $a_i\in\{1,2,3,4,5,6\}$. For each face $v$, let $f_v$ be its number of occurrences. Print $f_1,\ldots,f_6$.

Input

Line 1 contains $n$. Line 2 contains $a_1,\ldots,a_n$.

Output

Print the six values $f_1,f_2,\ldots,f_6$.

Subtasks

Subtask 1 (20 points): $1\le n\le 50$; $a_i\in\{1,2,3,4,5,6\}$.

Subtask 2 (30 points): $1\le n\le 5000$; $a_i\in\{1,2,3,4,5,6\}$.

Subtask 3 (50 points): $1\le n\le 100000$; $a_i\in\{1,2,3,4,5,6\}$.

Example

Input

8
1 6 2 6 6 3 1 4

Output

2 1 1 1 0 3

Explanation

The values follow directly from the definitions and illustrate the valid index range of the array scan.