Problem: There were n types of swords in the theater basement which had been used during the plays. Moreover there were exactly x swords of each type. y people have broken into the theater basement and each of them has taken exactly z swords of some single type. Note that different people might have taken different types of swords. Note that the values x, y and z are unknown for you.

The next morning the director of the theater discovers the loss. He counts all swords — exactly a_i swords of the i-th type are left untouched.

The director has no clue about the initial number of swords of each type in the basement, the number of people who have broken into the basement and how many swords each of them have taken.

For example, if n=3, a = [3, 12, 6] then one of the possible situations is x=12, y=5 and z=3. Then the first three people took swords of the first type and the other two people took swords of the third type. Note that you don't know values x, y and z beforehand but know values of n and a.

Thus he seeks for your help. Determine the minimum number of people y, which could have broken into the theater basement, and the number of swords z each of them has taken.

Input

The first line of the input contains one integer n (2 ≤ n ≤ 2 ⋅ 10^{5}) — the number of types of swords.

The second line of the input contains the sequence a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10^{9}), where a_i equals to the number of swords of the i-th type, which have remained in the basement after the theft. It is guaranteed that there exists at least one such pair of indices (j, k) that a_j ≠ a_k.

Output

Print two integers y and z — the minimum number of people which could have broken into the basement and the number of swords each of them has taken.

Examples

Input


3
3 12 6


Output


5 3


Input


2
2 9


Output


1 7


Input


7
2 1000000000 4 6 8 4 2


Output


2999999987 2


Input


6
13 52 0 13 26 52


Output


12 13

Note

In the first example the minimum value of y equals to 5, i.e. the minimum number of people who could have broken into the basement, is 5. Each of them has taken 3 swords: three of them have taken 3 swords of the first type, and two others have taken 3 swords of the third type.

In the second example the minimum value of y is 1, i.e. the minimum number of people who could have broken into the basement, equals to 1. He has taken 7 swords of the first type.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.math.*;
public class splset{
	static int mod = (int)1e9+7;
	public static PrintWriter out = new PrintWriter (new BufferedOutputStream(System.out));
	public static void main(String sp[])throws IOException{
		FastReader sc = new FastReader();
		int n = sc.nextInt();
		
		ArrayList<Long> al  = new ArrayList<>();
		for(int i=0;i<n;i++){
			al.add(sc.nextLong());
		}
		long max =0;
		for(int i=0;i<n;i++){
			max = Math.max(max,al.get(i));
		}
		long total=0;
		long r=0;
		for(int i=0;i<n;i++){
			r = gcd(r,max-al.get(i));
			total+=max-al.get(i);
		}
		long ans = total/r;
		System.out.println(ans+" "+r);
	}
	
	
	public static long calc(long num , long a, long b, long c){
		long lcmas  = (a*b)/gcd(a,b);
		long lcmbs  = (c*b)/gcd(c,b);
		long lcmcs  = (a*c)/gcd(a,c);
		long lcmll  = (lcmas*c)/gcd(c,lcmas);
		
		return (num/a)+(num/b)+(num/c)- (num/lcmas) - (num/lcmbs) - (num/lcmcs) + (num/lcmll);
		
	}
	
	
	
	
	
	//static HashMap<Integer,Integer> visited = new HashMap<>();
		
	
	/*public static int compute(int root, int n, int m, Tree[] edge, int values[]){
			
			LinkedList<Integer> ll = 	new LinkedList<>();
			ll.add(root);
				
			while(ll.size()>0){
				int val = ll.removeFirst();
				visited.put(val,0);
				ArrayList<Integer> al = edge[val].al;
				int length = al.size();
				for(int i=0;i<length;i++){
					ll.addLast(al.get(i));
					int hold = edge[val].weight+values[root];
					values[al.get(i)] = Math.min(hold,values[al.get(i)]);
				}
			}
			return values[n];
			
	}*/
	
	
	public static class Tree{
		int weight;
		int destination;
	}
	
	
	
	public static int partition(int [] arr, int s, int e){
		
		int index=s;
		int pivot = arr[e];
		for(int i=s;i<=e-1;i++){
			if(arr[i]<=pivot){
				arr = swap(arr, index, i);
				index++;
			}
		}
		swap(arr,index,e);
		print(arr);
		return index;
	}
	
	public static int[] swap(int[] arr, int low, int high){
		int temp = arr[low];
		arr[low]=arr[high];
		arr[high]=temp;
		return arr;
	}
	
	
	public static long gcd(long a, long b){
		if(b==0)
			return a;
		
		return gcd(b,a%b);
	}
	
	public static void print(int[] arr){
		for(int i=0;i<arr.length;i++)
			System.out.print(arr[i]+" ");
		System.out.println();
	}
	
	public static class pair{
		int val;
		int index;
	}
	
	public static class comp implements Comparator<pair>{
		public int compare(pair o1, pair o2){
			return o2.val-o1.val;
		}
	}
	public static class FastReader {
		BufferedReader br;
		StringTokenizer st;
	
 
		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}
 
		String next() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (Exception r) {
					r.printStackTrace();
				}
			}
			return st.nextToken();
		}
 
		int nextInt() {
			return Integer.parseInt(next());//converts string to integer
		}
 
		double nextDouble() {
			return Double.parseDouble(next());
		}
 
		long nextLong() {
			return Long.parseLong(next());
		}
 
		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (Exception r) {
				r.printStackTrace();
			}
			return str;
		}
	}
	
}