There is a matrix A of size x × y filled with integers. For every <image>, <image> Ai, j = y(i - 1) + j. Obviously, every integer from [1..xy] occurs exactly once in this matrix. 

You have traversed some path in this matrix. Your path can be described as a sequence of visited cells a1, a2, ..., an denoting that you started in the cell containing the number a1, then moved to the cell with the number a2, and so on.

From the cell located in i-th line and j-th column (we denote this cell as (i, j)) you can move into one of the following cells:

  1. (i + 1, j) — only if i < x; 
  2. (i, j + 1) — only if j < y; 
  3. (i - 1, j) — only if i > 1; 
  4. (i, j - 1) — only if j > 1.



Notice that making a move requires you to go to an adjacent cell. It is not allowed to stay in the same cell. You don't know x and y exactly, but you have to find any possible values for these numbers such that you could start in the cell containing the integer a1, then move to the cell containing a2 (in one step), then move to the cell containing a3 (also in one step) and so on. Can you choose x and y so that they don't contradict with your sequence of moves?

Input

The first line contains one integer number n (1 ≤ n ≤ 200000) — the number of cells you visited on your path (if some cell is visited twice, then it's listed twice).

The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the integers in the cells on your path.

Output

If all possible values of x and y such that 1 ≤ x, y ≤ 109 contradict with the information about your path, print NO.

Otherwise, print YES in the first line, and in the second line print the values x and y such that your path was possible with such number of lines and columns in the matrix. Remember that they must be positive integers not exceeding 109.

Examples

Input

8
1 2 3 6 9 8 5 2


Output

YES
3 3


Input

6
1 2 1 2 5 3


Output

NO


Input

2
1 10


Output

YES
4 9

Note

The matrix and the path on it in the first test looks like this:

<image>

Also there exist multiple correct answers for both the first and the third examples.
/*****Author: Satyajeet Singh, Delhi Technological University************************************/
    import java.io.*;
    import java.util.*;
    import java.text.*; 
    import java.lang.*;
    import java.math.*;
public class Main{
/*********************************************Constants******************************************/
    static PrintWriter out=new PrintWriter(new OutputStreamWriter(System.out));        
    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    static long mod=(long)1e9+7;
    static long mod1=998244353;
    static ArrayList<Integer> graph[];
    static int pptr=0,pptrmax=0;
    static String st[];
/*****************************************Solution Begins***************************************/    
    
    public static void main(String args[]) throws Exception{
        int n=pi();
        int input[]=new int[n];
        for(int i=0;i<n;i++){
            input[i]=pi();
        }
        boolean flag=false;
        HashSet<Integer> set=new HashSet<>();
        HashSet<Integer> set1=new HashSet<>();

        for(int i=0;i<n-1;i++){
            int a=Math.abs(input[i]-input[i+1]);
            if(a==0){
                flag=true;
            }
            if(a==1){
                set1.add(Math.min(input[i],input[i+1]));   
                continue;
            }
            set.add(a);
        }
        //debug(set1);

        if(set.size()<=1&&!flag){
            
            int ans=1;
            for(int u:set)ans=u;
            if(ans!=1){
                for(int u:set1){
                    if(u%ans==0){
                        out.println("NO");
                        out.flush();
                        out.close();
                        return;
                    }
                }
            }
            out.println("YES");
            int kk=(int)1e9;
            out.println(kk+" "+ans);
        }
        else{
            out.println("NO");
        }
/****************************************Solution Ends**************************************************/
        out.flush();
        out.close();
    }
/****************************************Template Begins************************************************/
    static void nl() throws Exception{
        pptr=0;
        st=br.readLine().split(" ");
        pptrmax=st.length;
    }
    static void nls() throws Exception{
        pptr=0;
        st=br.readLine().split("");
        pptrmax=st.length;
    }
    static int pi() throws Exception{
        if(pptr==pptrmax)
            nl();
        return Integer.parseInt(st[pptr++]);
    }
    static long pl() throws Exception{
        if(pptr==pptrmax)
            nl();
        return Long.parseLong(st[pptr++]);
    }
    static double pd() throws Exception{
        if(pptr==pptrmax)
            nl();
        return Double.parseDouble(st[pptr++]);
    }
    static String ps() throws Exception{
        if(pptr==pptrmax)
            nl();
        return st[pptr++];
    }
/***************************************Precision Printing**********************************************/
    static void printPrecision(double d){
        DecimalFormat ft = new DecimalFormat("0.0000000000"); 
        out.println(ft.format(d));
    }
/**************************************Bit Manipulation**************************************************/
    static int countBit(long mask){
        int ans=0;
        while(mask!=0){
            mask&=(mask-1);
            ans++;
        }
        return ans;
    }
/******************************************Graph*********************************************************/
    static void Makegraph(int n){
        graph=new ArrayList[n];
        for(int i=0;i<n;i++)
            graph[i]=new ArrayList<>();
    }
    static void addEdge(int a,int b){
        graph[a].add(b);
    }
    // static void addEdge(int a,int b,int c){
    //     graph[a].add(new Pair(b,c));
    // }    
/*********************************************PAIR********************************************************/
    static class Pair{
        int u;
        int v;
        public Pair(int u, int v) {
            this.u = u;
            this.v = v;
        }
        public int hashCode() {
            int hu = (int) (u ^ (u >>> 32));
            int hv = (int) (v ^ (v >>> 32));
            return 31 * hu + hv;
        }
        public boolean equals(Object o) {
            Pair other = (Pair) o;
            return u == other.u && v == other.v;
        }
        public String toString() {
            return "[u=" + u + ", v=" + v + "]";
        }
    }
/******************************************Long Pair*******************************************************/
    static class Pairl{
        long u;
        long v;
        public Pairl(long u, long v) {
            this.u = u;
            this.v = v;
        }
        public int hashCode() {
            int hu = (int) (u ^ (u >>> 32));
            int hv = (int) (v ^ (v >>> 32));
            return 31 * hu + hv;
        }
        public boolean equals(Object o) {
            Pairl other = (Pairl) o;
            return u == other.u && v == other.v;
        }
        public String toString() {
            return "[u=" + u + ", v=" + v + "]";
        }
    }
/*****************************************DEBUG***********************************************************/
    public static void debug(Object... o){
        System.out.println(Arrays.deepToString(o));
    }
/************************************MODULAR EXPONENTIATION***********************************************/
    static long modulo(long a,long b,long c){
        long x=1,y=a%c;
        while(b > 0){
            if(b%2 == 1)
                x=(x*y)%c;
            y = (y*y)%c;
            b = b>>1;
        }
        return  x%c;
    }
/********************************************GCD**********************************************************/
    static long gcd(long x, long y){
        if(x==0)
            return y;
        if(y==0)
            return x;
        long r=0, a, b;
        a = (x > y) ? x : y; 
        b = (x < y) ? x : y;
        r = b;
        while(a % b != 0){
            r = a % b;
            a = b;
            b = r;
        }
        return r;
    }
}