COCI '06 Contest 1 #1 Modulo

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Points: 3
Time limit: 1.0s
Memory limit: 32M

Problem type

Given two integers and , modulo is the remainder when dividing by . For example, the numbers , , and become , , and , modulo . Write a program that accepts numbers as input and outputs the number of distinct numbers in the input, if the numbers are considered modulo .

Input Specification

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

Output Specification

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

Sample Input 1

1
2
3
4
5
6
7
8
9
10

Sample Output 1

10

Explanation for Sample Output 1

The numbers modulo are , , , , , , , , and .

Sample Input 2

42
84
252
420
840
126
42
84
420
126

Sample Output 2

1

Explanation for Sample Output 2

All numbers modulo are .

Sample Input 3

39
40
41
42
43
44
82
83
84
85

Sample Output 3

6

Explanation for Sample Output 3

The numbers modulo are , , , , , , , , and . There are distinct numbers.