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.io.*;
import java.math.BigInteger;
import java.util.*;

public class Main {
	public static void main(String[] args) throws IOException {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		PrintWriter out = new PrintWriter(outputStream);
		InputReader in = new InputReader(inputStream);
		
//		for(int i=4;i<=4;i++) {
//			InputStream uinputStream = new FileInputStream("leftout.in");
//			String f = i+".in";
//			InputStream uinputStream = new FileInputStream(f);
//			InputReader in = new InputReader(uinputStream);
//			PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter("leftout.out")));
			Task t = new Task();
			t.solve(in, out);
			out.close();			
//		}
	}	
	
	static class Task {
		int times = 0;
		public void solve(InputReader in, PrintWriter out) throws IOException {
//			//int xxx = in.nextInt();
//			//while(xxx-->0) {
//				int n = in.nextInt();
//				int k = in.nextInt();
//				int a[] = in.readIntArray(n);
//				int b[] = in.readIntArray(n);
//				ArrayList<Integer>[] g = new ArrayList[n];
//				for(int i=0;i<n;i++) g[i] = new ArrayList<Integer>();
//				for(int i=0;i<n-1;i++) {
//					g[a[i]-1].add(a[i+1]-1);
//					g[b[i]-1].add(b[i+1]-1);
//				}
//				boolean vis[] = new boolean[n];
//				int lvl[] = new int[n];
//				int low[] = new int[n];
//				int hash[] = new int[n];
//				times = 0;
//				dfs(a[0]-1,g,vis,low,lvl,hash);
//				int cycles = 0; int cycle_nodes = 0;
//				DSU dsu = new DSU(n);
//				for(int i=0;i<n;i++) {
//					if(hash[low[i]]<i) {
//						dsu.union(hash[low[i]], i);
//					}else {
//						dsu.union(i,hash[low[i]]);
//					}
//				}
//				HashMap<Integer,Integer> s = new HashMap<Integer,Integer>();
//				for(int i=0;i<n;i++) {
//					int tmp = dsu.find(i);
//					s.put(tmp, s.getOrDefault(tmp, 0)+1);
//					//low[i] = s.get(dsu.find(i));
//				}
//				for(int i:s.keySet()) {
//					if(s.get(i)>1) {
//						cycles++;
//						cycle_nodes+=s.get(i);
//					}
//				}
//				if(k==3) {
//					//Dumper.print("here");
//				}
//				if(n-cycle_nodes+cycles>=k) {
//					System.out.println("YES");
//					//out.println("YES");
//					int temp [] = new int[n];
//					for(int i=0;i<n;i++) temp[i] = low[a[i]-1];
//					for(int i=1;i<n;i++) {
//						if(temp[i]>temp[i-1]+1) temp[i] = temp[i-1]+1;				
//						if(temp[i]>=k) temp[i] = temp[i-1];								
//					}
//					for(int i=0;i<n;i++) {
//						low[a[i]-1] = temp[i]; 
//					}
//					for(int i=0;i<n;i++) {
//						System.out.print((char)('a'+low[i]));
//						//out.print((char)('a'+low[i]));
//					}
//					System.out.println();
//					//out.println();
//				}
//				else {
//					System.out.println("NO");
//					//out.println("NO");	
//				}
//			//}
			int n = in.nextInt();
			long arr[] = new long[n];
			long max = 0;
			for(int i=0;i<n;i++) {
				arr[i] = in.nextLong();
				if(arr[i]>max) max=arr[i];
			}
			for(int i=0;i<n;i++) arr[i] = max-arr[i];
			long gcd = arr[0];
			for(int i=1;i<n;i++) {
				gcd = GCD(gcd, arr[i]);
			}
			long y = 0;
			for(int i=0;i<n;i++) {
				y+=arr[i]/gcd;
			}
			out.println(y+" "+gcd);
		}

	    
		class pair implements Comparable<pair>{
			int num, like, dlike;
			public pair(int b, int c, int d) {
				num=b;like=c;dlike=d;
			}
			public int compareTo(pair x) {
				return x.dlike-this.dlike;
			}
		}		
		
	    public int maxLength(List<String> arr) {
	    	int n = arr.size();
	    	int w[] = new int[n];
	        int[][] a = new int[n][26];
	        for(int i=0;i<n;i++) {
	        	String tmp = arr.get(i);
	        	w[i] = tmp.length();
	        	for(int j=0;j<tmp.length();j++) {
	        		a[i][tmp.charAt(j)-'a']++;
	        		if(a[i][tmp.charAt(j)-'a']>1) w[i]=0;
	        	}
	        }
	        boolean g[][] = new boolean[n][n];	       
	        for(int i=0;i<n;i++) {
	        	for(int j=i+1;j<n;j++) {
	        		boolean flag = false;
	        		for(int k=0;k<26;k++) {
	        			if(a[i][k]!=0&&a[j][k]!=0) flag = true; 
	        		}
	        		if(!flag) g[i][j] = g[j][i] = true;
	        	}
	        }
	        int max = 0;
	        for(int i=0;i<(1<<n);i++) {
	        	boolean flag = true;
	        	for(int j=0;j<n;j++) {if((i&(1<<j))==0) continue;
	        		if((i&(1<<j))==0||!flag) continue;
	        		for(int k=j+1;k<n;k++) {
	        			if((i&(1<<k))==0||!flag) continue;
	        			if(!g[j][k]) flag = false;
	        		}
	        	}
	        	if(!flag) continue;
	        	//Dumper.print(i);
	        	int s = 0;
	        	for(int j=0;j<n;j++) if((i&(1<<j))==(1<<j)) s+=w[j];
	        	if(s>max) max = s;
	        }
	        return max;
	    }

		
		int dfs(int cur, ArrayList<Integer>[] g, boolean vis[], int low[], int[] lvl, int hash[]) {
			lvl[cur] = low[cur] = times;
			hash[times] = cur;
			times++;
			int reach = low[cur];
			vis[cur] = true;
			for(int to:g[cur]) {
				if(vis[to]) {
					reach = Math.min(reach, low[to]);
				}else {
					int tmp = dfs(to,g,vis,low,lvl,hash);
					reach = Math.min(reach, tmp);
				}
			}
			if(reach<low[cur]) low[cur] = reach;
			return low[cur];
		}
		class edge implements Comparable<edge>{
			int f,t,l,s;
			public edge(int a, int b, int c) {
				if(a<b){
					f=a;t=b;
				}else {
					f=b;t=a;
				}
				l=c;
			}
			@Override
			public int compareTo(edge t) {
				return this.l-t.l;
			}			
		}


			    	
		List<List<Integer>> convert(int arr[][]){
			int n = arr.length;
			List<List<Integer>> ret = new ArrayList<>();
			for(int i=0;i<n;i++) {
				ArrayList<Integer> tmp = new ArrayList<Integer>();
				for(int j=0;j<arr[i].length;j++) tmp.add(arr[i][j]);
				ret.add(tmp);
			}
			return ret;
		}
		
	    public int maximumSum(int[] arr) {
	        int n = arr.length;
	        int dp[][] = new int[n][2];
	        dp[0][0] = arr[0];
	        int ret = arr[0];
	        for(int i=1;i<n;i++) {
	        	dp[i][0] = dp[i-1][0]>=0?(dp[i-1][0]+arr[i]):arr[i];
	        	int t1 = dp[i-1][0];
	        	int t2 = (dp[i-1][1]<0?0:dp[i-1][1])+arr[i];
	        	dp[i][1] = Math.max(t1,t2);
	        	ret = Math.max(ret,Math.max(dp[i][0], dp[i][1]));
	        } 
	        return ret;
	    }		
	    public List<Integer> findNumOfValidWords(String[] words, String[] puzzles) {
	        List<Integer> ret = new ArrayList<Integer>();
	        HashMap<Integer,Integer>[] mp = new HashMap[26];
	        for(int i=0;i<26;i++) mp[i] = new HashMap<Integer,Integer>();
	        //String p = "abcdz";
	        //Dumper.print(enc(p));
	        for(int i=0;i<words.length;i++) {
	        	int v = enc(words[i]);
	        	for(int j=0;j<words[i].length();j++) {
	        		mp[words[i].charAt(j)-'a'].put(v, 1);
	        	}
	        }
	        for(int i=0;i<puzzles.length;i++) {
	        	int n = puzzles[i].length();
	        	int t = 0;
	        	for(int j=1;j<1<<(n-1);j++) {
	        		int v = 0;
	        		for(int k=0;k<6;k++) {
	        			if((j&(1<<k))!=0) {
	        				v|=(1<<(puzzles[i].charAt(k)-'a'));
	        			}
	        		}
	        		v|=(1<<(puzzles[i].charAt(0)-'a'));   		
	        		//t+=search(v,mp[puzzles[i].charAt(0)-'a']);
	        	}
	        	ret.add(t);
	        }
	        return ret;
	    }	
	    int search(int x, HashMap<Integer,Integer> mp, HashSet<Integer> hs) {
	    	if(mp.containsKey(x)) return mp.get(x);
	    	if(x==0) return 0;
	    	int v = 0;
	    	for(int i=0;i<7;i++) {
	    		if((x&(1<<i))!=0) {
	    			int t = x;
	    			t^=(1<<i);
	    			if(!hs.contains(t)) {
	    				hs.add(t);
	    				v+=search(t,mp,hs);	    				
	    			}
	    		}
	    	}
	    	mp.put(x, v);	    	
	    	return v;
	    }
	    int enc(String x) {
	    	char[] arr = x.toCharArray();
	    	int v = 0;
	    	for(int i=0;i<arr.length;i++) {
	    		v|=1<<(arr[i]-'a');
	    	}
	    	return v;
	    }
		
		public class TreeNode {
			int val;
			TreeNode left;
			TreeNode right;
			TreeNode(int x) { val = x; }
		}
	
		public int GCD(int a, int b) {
		   if (b==0) return a;
		   return GCD(b,a%b);
		}
		public long GCD(long a, long b) {
			   if (b==0) return a;
			   return GCD(b,a%b);
			}		
	}
	
	
    static class ArrayUtils {
        static final long seed = System.nanoTime();
        static final Random rand = new Random(seed);

        public static void sort(int[] a) {
            shuffle(a);
            Arrays.sort(a);
        }

        public static void shuffle(int[] a) {
            for (int i = 0; i < a.length; i++) {
                int j = rand.nextInt(i + 1);
                int t = a[i];
                a[i] = a[j];
                a[j] = t;
            }
        }

    }	
	static class BIT{
		int arr[];
		int n;
		public BIT(int a) {
			n=a;
			arr = new int[n];
		}
		int sum(int p) {
			int s=0;
			while(p>0) {
				s+=arr[p];
				p-=p&(-p);
			}
			return s;
		}
		void add(int p, int v) {
			while(p<n) {
				arr[p]+=v;
				p+=p&(-p);
			}
		}
	}
	static class DSU{
		int[] arr;
		int[] sz;
		public DSU(int n) {
			arr = new int[n];
			sz = new int[n];
			for(int i=0;i<n;i++) arr[i] = i;
			Arrays.fill(sz, 1);
		}
		public int find(int a) {
			if(arr[a]!=a) arr[a] = find(arr[a]);
			return arr[a];
		}
		public void union(int a, int b) {
			int x = find(a);
			int y = find(b);
			if(x==y) return;
			arr[y] = x;
			sz[x] += sz[y];
		}
		public int size(int x) {
			return sz[find(x)];
		}
	}	
	static class MinHeap<Key> implements Iterable<Key> {
		private int maxN;
		private int n;
		private int[] pq;
		private int[] qp;
		private Key[] keys;
		private Comparator<Key> comparator;
		
		public MinHeap(int capacity){
			if (capacity < 0) throw new IllegalArgumentException();
			this.maxN = capacity;
			n=0;
			pq = new int[maxN+1];
			qp = new int[maxN+1];
			keys = (Key[]) new Object[capacity+1];
			Arrays.fill(qp, -1);
		}
		
		public MinHeap(int capacity, Comparator<Key> c){
			if (capacity < 0) throw new IllegalArgumentException();
			this.maxN = capacity;
			n=0;
			pq = new int[maxN+1];
			qp = new int[maxN+1];
			keys = (Key[]) new Object[capacity+1];
			Arrays.fill(qp, -1);
			comparator = c;
		}			
		public boolean isEmpty()	{ return n==0; 	}
		public int size()			{ return n;		}
		public boolean contains(int i) {
	        if (i < 0 || i >= maxN) throw new IllegalArgumentException();
	        return qp[i] != -1;
		}	
		public int peekIdx() {
	        if (n == 0) throw new NoSuchElementException("Priority queue underflow");
	        return pq[1];		
		}	
		public Key peek(){
			if(isEmpty()) throw new NoSuchElementException("Priority queue underflow");
			return keys[pq[1]];
		}
		public int poll(){
			if(isEmpty()) throw new NoSuchElementException("Priority queue underflow");
			int min = pq[1];
			exch(1,n--);
			down(1);
			assert min==pq[n+1];
			qp[min] = -1;
			keys[min] = null;		
			pq[n+1] = -1;
			return min;
		}
	    public void update(int i, Key key) {
	        if (i < 0 || i >= maxN) throw new IllegalArgumentException();
	        if (!contains(i)) {
	        	this.add(i, key);
	        }else {
	        	keys[i] = key;
	        	up(qp[i]);
	        	down(qp[i]);
	        }
	    }	
		private void add(int i, Key x){
	        if (i < 0 || i >= maxN) throw new IllegalArgumentException();
	        if (contains(i)) throw new IllegalArgumentException("index is already in the priority queue");
	        n++;
	        qp[i] = n;
	        pq[n] = i;
	        keys[i] = x;
	        up(n);
		}
		private void up(int k){
			while(k>1&&less(k,k/2)){
				exch(k,k/2);
				k/=2;
			}
		}
		private void down(int k){
			while(2*k<=n){
				int j=2*k;
				if(j<n&&less(j+1,j)) j++;
				if(less(k,j)) break;
				exch(k,j);
				k=j;
			}
		}
		
		public boolean less(int i, int j){
	        if (comparator == null) {
	            return ((Comparable<Key>) keys[pq[i]]).compareTo(keys[pq[j]]) < 0;
	        }
	        else {
	            return comparator.compare(keys[pq[i]], keys[pq[j]]) < 0;
	        }
		}

		public void exch(int i, int j){
	        int swap = pq[i];
	        pq[i] = pq[j];
	        pq[j] = swap;
	        qp[pq[i]] = i;
	        qp[pq[j]] = j;
		}

		@Override
		public Iterator<Key> iterator() {
			// TODO Auto-generated method stub
			return null;
		}
	}  	

    private static class InputReader
    {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int zcurChar;
        private int znumChars;
        private SpaceCharFilter filter;

        public InputReader(InputStream stream)
        {
            this.stream = stream;
        }

        public int read()
        {
            if (znumChars == -1)
                throw new InputMismatchException();
            if (zcurChar >= znumChars)
            {
            	zcurChar = 0;
                try
                {
                    znumChars = stream.read(buf);
                } catch (IOException e)
                {
                    throw new InputMismatchException();
                }
                if (znumChars <= 0)
                    return -1;
            }
            return buf[zcurChar++];
        }

        public int nextInt()
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public String nextString()
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do
            {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public double nextDouble()
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.')
            {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.')
            {
                c = read();
                double m = 1;
                while (!isSpaceChar(c))
                {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public long nextLong()
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c)
        {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next()
        {
            return nextString();
        }

        public interface SpaceCharFilter
        {
            public boolean isSpaceChar(int ch);
        }
        public int[] readIntArray(int n) {
            int[] ret = new int[n];
            for (int i = 0; i < n; i++) {
                ret[i] = nextInt();
            }
            return ret;
        }        
    }    

	static class Dumper {
		static void print_int_arr(int[] arr) {
			for (int i = 0; i < arr.length; i++) {
				System.out.print(arr[i] + " ");
			}
			System.out.println();
			System.out.println("---------------------");
		}

		static void print_char_arr(char[] arr) {
			for (int i = 0; i < arr.length; i++) {
				System.out.print(arr[i] + " ");
			}
			System.out.println();
			System.out.println("---------------------");
		}

		static void print_double_arr(double[] arr) {
			for (int i = 0; i < arr.length; i++) {
				System.out.print(arr[i] + " ");
			}
			System.out.println();
			System.out.println("---------------------");
		}

		static void print_2d_arr(int[][] arr, int x, int y) {
			for (int i = 0; i < x; i++) {
				for (int j = 0; j < y; j++) {
					System.out.print(arr[i][j] + " ");
				}
				System.out.println();
			}
			System.out.println();
			System.out.println("---------------------");
		}

		static void print_2d_arr(boolean[][] arr, int x, int y) {
			for (int i = 0; i < x; i++) {
				for (int j = 0; j < y; j++) {
					System.out.print(arr[i][j] + " ");
				}
				System.out.println();
			}
			System.out.println();
			System.out.println("---------------------");
		}

		static void print(Object o) {
			System.out.println(o.toString());
		}

		static void getc() {
			System.out.println("here");
		}
	}
}