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.util.*;
public class Main {
    public static void main(String[] args) throws Exception {
        new Main().run();}

    static int groups = 0;
    static int[] fa;
    static int[] sz;

    static void init1(int n) {
        groups = n;
        fa = new int[n];
        for (int i = 1; i < n; ++i) {
            fa[i] = i;
        }
        sz = new int[n];
        Arrays.fill(sz, 1);
    }

    static int root(int p) {
        while (p != fa[p]) {
            fa[p] = fa[fa[p]];
            p = fa[p];
        }
        return p;
    }

    static void combine(int p, int q) {
        int i = root(p);
        int j = root(q);
        if (i == j) {
            return;
        }
        if (sz[i] < sz[j]) {
            fa[i] = j;
            sz[j] += sz[i];
        } else {
            fa[j] = i;
            sz[i] += sz[j];
        }
        groups--;
    }


    public static String roundS(double result, int scale){
        String fmt = String.format("%%.%df", scale);
        return String.format(fmt, result);
    }

    int[] unique(int a[]){
        int p = 1;
        for(int i=1;i<a.length;++i){
            if(a[i]!=a[i-1]){
                a[p++] = a[i];
            }
        }
        return Arrays.copyOf(a,p);
    }
    public static int eq_bigger(int[] a, int key) {
        return eq_bigger(a,0,a.length,key);
    }

    public static int eq_bigger(int[] a, int lo, int hi,
                                int key) {
        while (lo < hi) {
            int mid = (lo + hi) >>> 1;
            if (a[mid] < key) {
                lo = mid + 1;
            }else {
                hi = mid;
            }
        }
        return lo;
    }

    public static int bigger(int[] a, int key) {
        return bigger(a,0,a.length,key);
    }

    public static int bigger(int[] a, int lo, int hi,
                             int key) {
        while (lo < hi) {
            int mid = (lo + hi) >>> 1;
            if (a[mid] > key) {
                hi = mid;
            }else {
                lo = mid+1;
            }
        }
        return lo;
    }


    static int h[];
    static int to[];
    static int ne[];
    static int m = 0;

    public static void addEdge(int u, int v, int w) {
        to[++m] = v; ne[m] = h[u]; h[u] = m;
    }



    long w[];

    int cc = 0;

    void add(int u,int v,long ww) {
        to[++cc] = u;
        w[cc] = ww;
        ne[cc] = h[v];
        h[v] = cc;

        to[++cc] = v;
        w[cc] = ww;
        ne[cc] = h[u];
        h[u] = cc;
    }

    boolean isin(long z1[],long z2[]){
        return z2[0]<=z1[0]&&z2[1]<=z1[1]&&z2[2]>=z1[2]&&z2[3]>=z1[3];
    }

    boolean pisin(long p[],long z2[]){
        return z2[0]<=p[0]&&z2[1]<=p[1]&&z2[2]>=p[0]&&z2[3]>=p[1];
    }

    void solve() {

        int n = ni();
        long a[] = nal(n);
        Arrays.sort(a);
        long d[] = new long[n-1];
        for(int i = 0;i<n-1;++i){
           long f =  a[i+1]-a[i];
           d[i] = f;
        }
        long z = 0;
        for(int i=0;i<n-1;++i){
            z = gcd(z,d[i]);
        }
        long f[] = new long[n];
        f[n-2] = d[n-2]/z;
        long an = f[n-2];
        for(int i=n-3;i>=0;--i){
            f[i] = d[i]/z+f[i+1];
            an += f[i];
        }
println(an+" "+z);










    }




















































    static class S{
        int l = 0;
        int r = 0 ;
        int idx = 0;
        long all = 0;

        public S(int l,int r) {
            this.l = l;
            this.r = r;
        }
    }

    static S a[];
    static int[] o;

    static void init(int[] f){
        o = f;
        int len = o.length;
        a = new S[len*4];
        build(1,0,len-1);
    }

    static void build(int num,int l,int r){
        S cur = new S(l,r);
        if(l==r){
            a[num] = cur;
            a[num].all = o[l];
            a[num].idx = l;
            return;
        }else{
            int m = (l+r)>>1;
            int le = num<<1;
            int ri = le|1;
            build(le, l,m);
            build(ri, m+1,r);
            a[num] = cur;
            pushup(num, le, ri);
        }
    }



    static int[] query(int num,int l,int r){

        if(a[num].l>=l&&a[num].r<=r){
            return new int[]{a[num].idx,(int)a[num].all};
        }else{
            int m = (a[num].l+a[num].r)>>1;
            int le = num<<1;
            int ri = le|1;
            //   pushdown(num, le, ri);
            int ma = -1;
            int idx = 100000001;
            if(l<=m) {
                int r1[] = query(le, l, r);
                if(r1[1]>ma){
                    ma = r1[1];
                    idx = r1[0];
                }

            }
            if(r>m){
                int r2[] = query(ri, l, r);
                if(r2[1]>ma){
                    ma = r2[1];
                    idx = r2[0];
                }
            }
            return new int[]{idx,ma};
        }
    }


    static void update(int num,int l,long v){
        if(a[num].l==a[num].r){
            a[num].all = v;
        }else{
            int m = (a[num].l+a[num].r)>>1;
            int le = num<<1;
            int ri = le|1;
            pushdown(num, le, ri);
            if(l<=m){
                update(le,l,v);
            }
            if(l>m){
                update(ri,l,v);
            }
            pushup(num,le,ri);
        }
    }

    static void pushup(int num,int le,int ri){
        a[num].all = Math.max(a[le].all,a[ri].all);
        if(a[le].all>a[ri].all){
            a[num].idx = a[le].idx;
        }else{
            a[num].idx = a[ri].idx;
        }

    }
    static void pushdown(int num,int le,int ri){

    }


    long gcd(long a,long b){ return b==0?a: gcd(b,a%b);}
    InputStream is;PrintWriter out;
    void run() throws Exception {is = System.in;out = new PrintWriter(System.out);solve();out.flush();}
    private byte[] inbuf = new byte[1024];
    public int lenbuf = 0, ptrbuf = 0;
    private int readByte() {
        if (lenbuf == -1) throw new InputMismatchException();
        if (ptrbuf >= lenbuf) {
            ptrbuf = 0;
            try {lenbuf = is.read(inbuf);} catch (IOException e) {throw new InputMismatchException();}
            if (lenbuf <= 0) return -1;
        }
        return inbuf[ptrbuf++];}
    private boolean isSpaceChar(int c) {return !(c >= 33 && c <= 126);}
    private int skip() {int b;while((b = readByte()) != -1 && isSpaceChar(b));return b;}
    private double nd() {return Double.parseDouble(ns());}
    private char nc() {return (char) skip();}
    private char ncc() {int b;while((b = readByte()) != -1 && !(b >= 32 && b <= 126));return (char)b;}
    private String ns() {int b = skip();StringBuilder sb = new StringBuilder();
        while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);b = readByte(); }
        return sb.toString();}
    private char[] ns(int n) {char[] buf = new char[n];int b = skip(), p = 0;
        while (p < n && !(isSpaceChar(b))) { buf[p++] = (char) b;b = readByte(); }
        return n == p ? buf : Arrays.copyOf(buf, p);}
    private String nline() {int b = skip();StringBuilder sb = new StringBuilder();
        while (!isSpaceChar(b) || b == ' ') { sb.appendCodePoint(b);b = readByte(); }
        return sb.toString();}
    private char[][] nm(int n, int m) {char[][] a = new char[n][];for (int i = 0; i < n; i++) a[i] = ns(m);return a;}
    private int[] na(int n) {int[] a = new int[n];for (int i = 0; i < n; i++) a[i] = ni();return a;}
    private long[] nal(int n) { long[] a = new long[n];for (int i = 0; i < n; i++) a[i] = nl();return a;}
    private int ni() { int num = 0, b; boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')){};
        if (b == '-') { minus = true; b = readByte(); }
        while (true) {
            if (b >= '0' && b <= '9') num = (num << 3) + (num << 1) + (b - '0');
            else return minus ? -num : num;
            b = readByte();}}
    private long nl() { long num = 0; int b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')){};
        if (b == '-') { minus = true; b = readByte(); }
        while (true) {
            if (b >= '0' && b <= '9')  num = num * 10 + (b - '0');
            else return minus ? -num : num;
            b = readByte();}}
    void print(Object obj){out.print(obj);}
    void println(Object obj){out.println(obj);}
    void println(){out.println();}
}