[백준] 2485 가로수

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import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Main {
	static int min = 1111111111;
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int result = 0;
		int N = Integer.parseInt(br.readLine());
		int[] arr = new int[N];
		int[] distance = new int[N-1];
		arr[0] = Integer.parseInt(br.readLine());
		for(int i = 1; i < N; i++) {
			arr[i] = Integer.parseInt(br.readLine());
			distance[i-1] = arr[i] - arr[i-1];
			min = Math.min(min, distance[i-1]);
		}
		for(int i = 0; i < N-1; i++) {
			min = gcd(distance[i], min);
		}
		System.out.println(result(distance, N, min));
	}
	static int result(int[] arr,int N, int dis) {
		int ans = 0;
		for(int i = 0; i < N-1; i++) {
			ans += arr[i]/dis - 1;
		}
		return ans;
	}
	static int gcd(int bn, int sn) {
		int r = bn % sn;
		
		if(r == 0) {
			return sn;
		}
		else {
			return gcd(sn, r);
		}
	}
}