Given two integers $A$ and $B$, $A$ modulo $B$ is the remainder when dividing $A$ by $B$. For example, the numbers $7$, $14$, $27$ and $38$ become $1$, $2$, $0$ and $2$, modulo $3$. Write a program that accepts $10$ numbers as input and outputs the number of distinct numbers in the input, if the numbers are considered modulo $42$.

-----Input-----
The input will contain 10 non-negative integers, each smaller than $1000$, one per line.

-----Output-----
Output the number of distinct values when considered modulo $42$ on a single line.

-----Explanation of Sample Inputs-----
In sample input $1$, the numbers modulo $42$ are $1, 2, 3, 4, 5, 6, 7, 8, 9$ and $10$.

In sample input $2$, all numbers modulo $42$ are $0$.

In sample input $3$, the numbers modulo $42$ are $39, 40, 41, 0, 1, 2, 40, 41, 0$ and $1$. There are $6$ distinct numbers.

-----Examples-----
Sample Input 1:
1
2
3
4
5
6
7
8
9
10
Sample Output 1:
10

Sample Input 2:
42
84
252
420
840
126
42
84
420
126
Sample Output 2:
1

Source: kattis | Difficulty: EASY
Tags: Mathematics


Solutions: