Iahub is a big fan of tourists. He wants to become a tourist himself, so he planned a trip. There are n destinations on a straight road that Iahub wants to visit. Iahub starts the excursion from kilometer 0. The n destinations are described by a non-negative integers sequence a1, a2, ..., an. The number ak represents that the kth destination is at distance ak kilometers from the starting point. No two destinations are located in the same place. 

Iahub wants to visit each destination only once. Note that, crossing through a destination is not considered visiting, unless Iahub explicitly wants to visit it at that point. Also, after Iahub visits his last destination, he doesn't come back to kilometer 0, as he stops his trip at the last destination. 

The distance between destination located at kilometer x and next destination, located at kilometer y, is |x - y| kilometers. We call a "route" an order of visiting the destinations. Iahub can visit destinations in any order he wants, as long as he visits all n destinations and he doesn't visit a destination more than once. 

Iahub starts writing out on a paper all possible routes and for each of them, he notes the total distance he would walk. He's interested in the average number of kilometers he would walk by choosing a route. As he got bored of writing out all the routes, he asks you to help him.

Input

The first line contains integer n (2 ≤ n ≤ 105). Next line contains n distinct integers a1, a2, ..., an (1 ≤ ai ≤ 107).

Output

Output two integers — the numerator and denominator of a fraction which is equal to the wanted average number. The fraction must be irreducible.

Examples

Input

3
2 3 5


Output

22 3

Note

Consider 6 possible routes:

  * [2, 3, 5]: total distance traveled: |2 – 0| + |3 – 2| + |5 – 3| = 5; 
  * [2, 5, 3]: |2 – 0| + |5 – 2| + |3 – 5| = 7; 
  * [3, 2, 5]: |3 – 0| + |2 – 3| + |5 – 2| = 7; 
  * [3, 5, 2]: |3 – 0| + |5 – 3| + |2 – 5| = 8; 
  * [5, 2, 3]: |5 – 0| + |2 – 5| + |3 – 2| = 9; 
  * [5, 3, 2]: |5 – 0| + |3 – 5| + |2 – 3| = 8. 



The average travel distance is <image> = <image> = <image>.
import java.io.BufferedReader;
import java.io.FileReader;
import java.io.IOException; 
import java.io.InputStreamReader; 
import java.util.Scanner; 
import java.util.StringTokenizer; 
import java.util.*;
import java.io.*;
public class codeforces 
{ 
   static class Student{
       int x,y,z;
        Student(int x,int y,int z){
            this.x=x;
            this.y=y;
            this.z=z;
        }
    }
    static int prime[];
    static void sieveOfEratosthenes(int n) 
    { 
        // Create a boolean array "prime[0..n]" and initialize 
        // all entries it as true. A value in prime[i] will 
        // finally be false if i is Not a prime, else true. 
        int pos=0;
        prime= new int[n+1]; 
        for(int p = 2; p*p <=n; p++) 
        { 
            // If prime[p] is not changed, then it is a prime 
            if(prime[p] == 0)
            { 
                // Update all multiples of p
                prime[p]=p;
                for(int i = p*p; i <= n; i += p)
                    if(prime[i]==0)
                    prime[i] = p; 
            } 
        } 
    }
static    class Sortbyroll implements Comparator<Student> 
{ 
    // Used for sorting in ascending order of 
    // roll number 
    public int compare(Student c, Student b) 
    { 
        return c.x-b.x;
    } 
} 
static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    } 
 
    static class Edge{
        int a,b;
        Edge(int a,int b){
            this.a=a;
            this.b=b;
        }
    }
    static class Trie{
        HashMap<Character,Trie>map;
         int c;
        Trie(){
            map=new HashMap<>();
            //z=null;
            //o=null;
            c=0;
        }
    }
    //static long ans;
    static int parent[];
    static int rank[];
    static int b[][];
    static int bo[];
    static int ho[];
    static int seg[];
    //static int pos;
   // static long mod=1000000007;
    //static int dp[][];
    static HashMap<Integer,Integer>map;
    static PriorityQueue<Student>q=new PriorityQueue<>();
    //static Stack<Integer>st;
   // static ArrayList<Character>ans;
    static ArrayList<ArrayList<Integer>>adj;
    //static long ans;
    static Trie root;
    static long fac[];
    static int gw,gb;
    static long mod=(long)(1000000007);
    //static int ans;
    static void solve()throws IOException{
        FastReader sc=new FastReader();
        int n,i;
        n=sc.nextInt();
        long a[]=new long[n];
        for(i=0;i<n;i++)
            a[i]=sc.nextLong();
        Arrays.sort(a);
        long sum=0,g;
        for(i=0;i<n;i++){
            sum+=-(long)(n-i-1)*a[i]+a[i]*(long)i;
        }
        sum=(long)2*sum;
        for(i=0;i<n;i++)
            sum+=a[i];
        g=gcd(sum,n);
        System.out.println((sum/g)+" "+((long)n/g));
    }
   static int tr(int i,int n,int dp[][],int a[],int h,int l,int r,int in){
        if(i>=n)
            return 0;
        if(dp[i][in]!=-1)
            return dp[i][in];
        int mod1,mod2,ans1=0,ans2=0;
        mod1=(a[i]+in)%h;
        if(mod1>=l&&mod1<=r)
            ans1=1+tr(i+1,n,dp,a,h,l,r,mod1);
        else
            ans1=tr(i+1,n,dp,a,h,l,r,mod1);
        mod2=(a[i]+in-1)%h;
        if(mod2>=l&&mod2<=r)
            ans2=1+tr(i+1,n,dp,a,h,l,r,mod2);
        else
            ans2=tr(i+1,n,dp,a,h,l,r,mod2);
        dp[i][in]=Math.max(ans1,ans2);
        return dp[i][in];
    }
    static long nCr(long n, long r, 
                                    long p) 
    { 
        return (fac[(int)n]* modInverse(fac[(int)r], p) 
                % p * modInverse(fac[(int)(n-r)], p) 
                                    % p) % p; 
    } 
    //static int prime[];
    //static int dp[];
    public static void main(String[] args){
        //long sum=0;
        try {
                codeforces.solve();
                } catch (Exception e) {
                    e.printStackTrace();
                }
    }
       static long modInverse(long n, long p) 
    { 
        return power(n, p-(long)2,p); 
    } 
 static long power(long x, long y, long p) 
{ 
    long res = 1;      // Initialize result 
  
    x = x % p;  // Update x if it is more than or  
                // equal to p 
  
    while (y > 0) 
    { 
        // If y is odd, multiply x with result 
        if (y %(long)2!=0) 
            res = (res*x) % p; 
  
        // y must be even now 
        y = y>>1; // y = y/2 
        x = (x*x) % p;   
    } 
    return res%p;
 }
    /*public static long power(long x,long a) {
		if(a==0) return 1;
		if(a%2==1)return (x*1L*power(x,a-1))%mod;
		return (power((int)((x*1L*x)%mod),a/2))%mod;
	}*/
   static int find(int x) 
    { 
        // Finds the representative of the set 
        // that x is an element of 
        while(parent[x]!=x) 
        { 
            // if x is not the parent of itself 
            // Then x is not the representative of 
            // his set,
            x=parent[x];
  
            // so we recursively call Find on its parent 
            // and move i's node directly under the 
            // representative of this set 
        } 
  
        return x; 
    }
    static void union(int x, int y) 
    { 
        // Find representatives of two sets 
        int xRoot = find(x), yRoot = find(y); 
  
        // Elements are in the same set, no need 
        // to unite anything. 
        if (xRoot == yRoot) 
            return; 
  
         // If x's rank is less than y's rank 
        if (rank[xRoot] < rank[yRoot]) 
  
            // Then move x under y  so that depth 
            // of tree remains less 
            parent[xRoot] = yRoot; 
  
        // Else if y's rank is less than x's rank 
        else if (rank[yRoot] < rank[xRoot]) 
  
            // Then move y under x so that depth of 
            // tree remains less 
            parent[yRoot] = xRoot; 
  
        else // if ranks are the same 
        { 
            // Then move y under x (doesn't matter 
            // which one goes where) 
            parent[yRoot] = xRoot; 
  
            // And increment the the result tree's 
            // rank by 1 
            rank[xRoot] = rank[xRoot] + 1; 
        } 
    } 
    static long gcd(long a, long b) 
    { 
        if (a == 0){ 
             //ans+=b;
            return b;
        }
        return gcd(b % a, a); 
    }
}