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.
import java.util.*;
import java.io.*;
import java.io.FileWriter; 
import java.math.BigInteger;
import java.math.BigDecimal;
// Solution

public class Main 
{    
  public static void main (String[] argv) 
  {
	  new Main();
  } 
     
  
  boolean test = false;  
  final int[][] dirs8 = {{0,1}, {0,-1}, {-1,0}, {1,0}, {1,1},{1,-1},{-1,1},{-1,-1}};
  final int[][] dirs4 = {{0,1}, {0,-1}, {-1,0}, {1,0}};
  final int MOD = 1000000007;  //998244353;

  
  
  final int WALL = -1;
  final int EMPTY = -2;
  final int VISITED = 1;
  final int FULL = 2;
  
  final int START = 1;
  final int END = 0;
  
  long[] fac;
  //long[] ifac;
  
  
  //long[] fac = new long[100];
  //long[] ifac = new long[100001];
  public Main()   {
	FastReader in = new FastReader(new BufferedReader(new InputStreamReader(System.in)));
	
     
   // FastReader in = new FastReader(new BufferedReader(new FileReader("Main.in")));   
    
    //int nt = in.nextInt();    
    int nt = 1;
    StringBuilder sb = new StringBuilder();
    
    //fac[0] = 1;
    //ifac[0] = 1;
    //for (int i = 1; i <= 20; i++) {
      //  fac[i] = fac[i-1] * i % MOD;
      //  ifac[i] = ifac[i-1] * inv(i) % MOD;
    //}
    long[][] C = new long[19][11];
    
    
    // Caculate value of Binomial Coefficient 
    // in bottom up manner 
    for (int i = 0; i <= 18; i++) 
    { 
        for (int j = 0; j <= min(i, 10); j++) 
        { 
            // Base Cases 
            if (j == 0 || j == i) 
                C[i][j] = 1; 
  
            // Calculate value using previously 
            // stored values 
            else
                C[i][j] = C[i - 1][j - 1] + 
                          C[i - 1][j]; 
        } 
    }
    
    
    //long[] invs = new long[101];
    //for (int i = 1; i <= 100; i++) invs[i] = inv(i);    
    
    for (int it = 0; it < nt; it++) 
    {        
       int n = in.nextInt();
       int[] a = new int[n];
       int maxVal = 0;
       for (int i = 0; i < n; i++)
       {
           a[i] = in.nextInt() - 1;
           maxVal = Math.max(maxVal, a[i]);
       }
       int y = -1;
       
       for (int i = 1; i < n; i++)
       {
           int diff = Math.abs(a[i] - a[i-1]);
           if (diff == 0) {
               System.out.println("NO");
               return;
           }else if (diff > 1)
           {
               if (y > 0 && diff != y) {
                   System.out.println("NO");
                   return;
               }else y = diff;
           }
       }
       
       //we already have y
       if (y < 0) y = 1;
       
       int x = maxVal / y + 1;
       
       //System.out.println("x = " + x + " , y = " + y);
       //now simulate       
       for (int i = 1; i < n; i++)
       {
           if (!connected(a[i], a[i-1], y)) {
               System.out.println("NO");
               return;
           }
       }
       
       sb.append("YES\n" + x + " " + y + "\n");
       
    }
    
    System.out.print(sb);
  }
  
  private boolean connected(int p, int q, int m) {
      int x1 = p / m, y1 = p % m;
      int x2 = q / m, y2 = q % m;
      if (x1 == x2) {
          return y1 + 1 == y2 || y1 - 1 == y2;
      }
      return y1 == y2 && ((x1 + 1 == x2) || (x1 - 1) == x2);
  }
  
  
  
  private long[][] matIdentity(int n)
  {
      long[][] a = new long[n][n];
      for (int i = 0; i < n; i++)
          a[i][i] = 1;
      return a;
  }
  private long[][] matPow(long[][] mat0, long p)
  {
      int n = mat0.length;
      long[][] ans = matIdentity(n);
      long[][] mat = matCopy(mat0);
      while (p > 0)
      {
          if (p % 2 == 1){
              ans = matMul(ans, mat);
          }
          
          p /= 2;
          mat = matMul(mat, mat);
      }
      return ans;
  }
  
  private long[][] matCopy(long[][] a)
  {
      int n = a.length;
      long[][] b = new long[n][n];
      for (int i = 0; i < n; i++)
          for (int j = 0; j < n; j++)
              b[i][j] = a[i][j];
      return b;
  }
  private long[][] matMul(long[][] a, long[][] b)
  {
      int n = a.length;
      
      long[][] c = new long[n][n];
      for (int i = 0; i < n; i++)
      {
          for (int j = 0; j < n; j++)
          {
              for (int k = 0; k < n; k++)
                  c[i][j] = (c[i][j] + a[i][k] * b[k][j]) % MOD;
          }
      }
      
      return c;
  }
  
  private long[] matMul(long[][] a, long[] b)
  {
      int n = a.length;
      
      long[] c = new long[n];
      for (int i = 0; i < n; i++)
      {
          for (int j = 0; j < n; j++)
              c[i] = (c[i] + a[i][j] * b[j]) % MOD;
      }
      
      return c;
  }
  
  class Mark implements Comparable<Mark> {
      int type, h;
      long x;
      public Mark(int h, long x, int type)
      {
         this.h = h;
         this.x = x;
         this.type = type;
      }      
      
      @Override
      public int compareTo(Mark o)
      {
          if (this.x == o.x) return type - o.type; // let end comes before start
          return Long.compare(x, o.x); 
      }
  }
  
  private boolean coLinear(int[] p, int[] q, int[] r)
  {
      return 1L * (p[1] - r[1]) * (q[0] - r[0]) == 1L * (q[1] - r[1]) * (p[0] - r[0]);
  }
  
  
  private void fill(char[] a, int lo, int c, char letter)
  {
      //System.out.println("fill " + lo + " " + c + " " + letter);
      for (int i = lo; i < lo + c; i++) a[i] = letter;
  }
  
  
  
  private int cntBitOne(String s){
      int c = 0, n = s.length();
      for (int i = 0; i < n; i++) 
          if (s.charAt(i) == '1') c++;
      return c;
  }
  
  class DSU {
      int n;
      int[] par;
      int[] sz;
      int nGroup;
      
      public DSU(int n)
      {
          this.n = n;
          par = new int[n];
          sz = new int[n];
          for (int i = 0;  i < n; i++){
              par[i] = i;
              sz[i] = 1;
          }
          nGroup = n;          
      }
      
      private boolean add(int p, int q) {
          int rp = find(p);
          int rq = find(q);
          if (rq == rp) return false;
          
          if (sz[rp] <= sz[rq]) {
              sz[rq] += sz[rp];
              par[rp] = rq;
          }else {
              sz[rp] += sz[rq];
              par[rq] = rp;
          }
          nGroup--;
          return true;
      }
      
      private int find(int p)
      {
          int r = p;
          while (par[r] != r) r = par[r];
          
          while (r != p) {
              int t = par[p];
              par[p] = r;
              p = t;
          }
          return r;
      }
      
  }
  
  private int[] build_z_function(String s)
  {
      int n = s.length();
      int[] zfun = new int[n];
      
      int l = -1, r = -1;
      for (int i = 1; i < n; i++)
      {
         // Set the start value
         if (i <= r)
            zfun[i] = Math.min(zfun[i-l], r - i + 1);
         
         while (i + zfun[i] < n && s.charAt(i + zfun[i]) == s.charAt(zfun[i])) 
             zfun[i]++;             
         
         if (i + zfun[i] - 1> r){
             l = i;
             r = i + zfun[i] - 1;
         }
      }
      
      if (test)
      {
          System.out.println("Z-function of " + s);
          for (int i = 0; i < n; i++) System.out.print(zfun[i] + " ");
          System.out.println();
      }
      return zfun;
  }
  
  class BIT {
      int[] bit;
      int n;
      
      public BIT(int n){
          this.n = n;
          bit = new int[n+1];
      }
      
      private int query(int p)
      {
          int sum = 0;
          for (; p > 0; p -= (p & (-p)))
             sum += bit[p];
      
          return sum;
      }
  
      private void add(int p, int val)
      {
         //System.out.println("add to BIT " + p);
         for (; p <= n; p += (p & (-p)))
            bit[p] += val;
      }
  
  
  }
  
  
  
  private List<Integer> getMinFactor(int sum)
  {
      List<Integer>  factors = new ArrayList<>();
      
               for (int sz = 2; sz <= sum / sz; sz++){
                   if (sum % sz == 0) {
                       factors.add(sz);
                       factors.add(sum / sz);
                   }
               }
               if (factors.size() == 0)
                   factors.add(sum);
          
      return factors;
  }
  
  /* Tree class */
  class Tree {
      int V = 0;
      int root = 0;
      List<Integer>[] nbs;
      int[][] timeRange;
      int[] subTreeSize;
      int t;
      boolean dump = false;
      
      public Tree(int V, int root)
      {
          if (dump) 
              System.out.println("build tree with size = " + V + ", root = " + root); 
          
          this.V = V;          
          this.root = root;
          nbs = new List[V];
          subTreeSize = new int[V];
          for (int i = 0; i < V; i++)
              nbs[i] = new ArrayList<>();
          
              
      }
      
      public void doneInput()
      {
          dfsEuler();
      }
      
      public void addEdge(int p, int q)
      {
          nbs[p].add(q);
          nbs[q].add(p);
      }
      
      private void dfsEuler()
      {
          timeRange = new int[V][2];          
          t = 1;
          dfs(root);           
      }
      
      private void dfs(int node)
      {
          if (dump)
              System.out.println("dfs on node " + node + ", at time " + t);
          timeRange[node][0] = t;
          
          for (int next : nbs[node]) {
              if (timeRange[next][0] == 0)
              {
                  ++t;
                  dfs(next);                  
              }
          }
          timeRange[node][1] = t;
          subTreeSize[node] = t - timeRange[node][0] + 1;
      }
      
      public List<Integer> getNeighbors(int p) {
          return nbs[p];
      }
      
      public int[] getSubTreeSize(){
          return subTreeSize;
      }
      
      public int[][] getTimeRange()
      {
          if (dump){
              for (int i = 0; i < V; i++){
                  System.out.println(i + ": " + timeRange[i][0] + " - " + timeRange[i][1]);
              }
          }
          return timeRange;
      }
      
  }
  
  /* segment tree */
  class SegTree {
      int[] a;
      int[] tree;
      int[] treeMin;
      int[] treeMax;
      int[] lazy;
      int n;
      boolean dump = false;
      
      public SegTree(int n)
      {
          if (dump)
              System.out.println("create segTree with size " + n);
          this.n = n;
          treeMin = new int[n*4];
          treeMax = new int[n*4];
          lazy = new int[n*4];
      }
      
      public SegTree(int n, int[] a) {
          this(n);
          this.a = a;
          buildTree(1, 0, n-1);          
      }
      
      private void buildTree(int node, int lo, int hi)
      {
          if (lo == hi) {
              tree[node] = lo;
              return;
          }
          
          int m = (lo + hi) / 2;
          buildTree(node * 2, lo, m);
          buildTree(node * 2 + 1, m + 1, hi);
          pushUp(node, lo, hi);
      }
      
      
      private void pushUp(int node, int lo, int hi)
      {
          if (lo >= hi) return;
          
          // note that, if we need to call pushUp on a node, then lazy[node] must be zero.
          
          //the true value is the value + lazy
          treeMin[node] = Math.min(treeMin[node * 2] + lazy[node * 2], treeMin[node * 2 + 1] + lazy[node * 2 + 1]);
          treeMax[node] = Math.max(treeMax[node * 2] + lazy[node * 2], treeMax[node * 2 + 1] + lazy[node * 2 + 1]);
          // add combine fcn
      }
      
      private void pushDown(int node, int lo, int hi)
      {
          if (lazy[node] == 0) return;
          
          int lz = lazy[node];
          lazy[node] = 0;          
          
          
          treeMin[node] += lz;
          treeMax[node] += lz;     
          
          if (lo == hi) return;
          
          int mid = (lo + hi) / 2;
          lazy[node * 2] += lz;
          lazy[node * 2 + 1] += lz;
      }
      
      public int rangeQueryMax(int fr, int to)
      {
          return rangeQueryMax(1, 0, n-1, fr, to);
      }
      
      public int rangeQueryMax(int node, int lo, int hi, int fr, int to)
      {
          if (lo == fr && hi == to)
              return treeMax[node] + lazy[node];
          
          int mid = (lo + hi) / 2;
          pushDown(node, lo, hi);
          
          if (to <= mid) {
              return rangeQueryMax(node * 2, lo, mid, fr, to);
          }else if (fr > mid)
              return rangeQueryMax(node * 2 + 1, mid + 1, hi, fr, to);
          else {
              return Math.max(rangeQueryMax(node * 2, lo, mid, fr, mid),
                              rangeQueryMax(node * 2 + 1, mid + 1, hi, mid + 1, to));              
          }
      }
      
      public int rangeQueryMin(int fr, int to)
      {
          return rangeQueryMin(1, 0, n-1, fr, to);
      }
      
      public int rangeQueryMin(int node, int lo, int hi, int fr, int to)
      {
          if (lo == fr && hi == to)
              return treeMin[node] + lazy[node];
          
          int mid = (lo + hi) / 2;
          pushDown(node, lo, hi);
          
          if (to <= mid) {
              return rangeQueryMin(node * 2, lo, mid, fr, to);
          }else if (fr > mid)
              return rangeQueryMin(node * 2 + 1, mid + 1, hi, fr, to);
          else {
              return Math.min(rangeQueryMin(node * 2, lo, mid, fr, mid),
                              rangeQueryMin(node * 2 + 1, mid + 1, hi, mid + 1, to));              
          }
      }
      
       public void rangeUpdate(int fr, int to, int delta){
           rangeUpdate(1, 0, n-1, fr, to, delta);
       }
       
       
      public void rangeUpdate(int node, int lo, int hi, int fr, int to, int delta){
          pushDown(node, lo, hi);
          if (fr == lo && to == hi)
          {
              lazy[node] = delta;
              return;
          }
          
          int m = (lo + hi) / 2;
          if (to <= m) 
              rangeUpdate(node * 2, lo, m, fr, to, delta);
          else if (fr > m)
              rangeUpdate(node * 2 + 1, m + 1, hi, fr, to, delta);
          else  {
              rangeUpdate(node *  2, lo, m, fr, m, delta);
              rangeUpdate(node * 2 + 1, m + 1, hi, m + 1, to, delta);              
          }
          
          // re-set the in-variant
          pushUp(node, lo, hi);
      }
      
      
      
      public int query(int node, int lo, int hi, int fr, int to)
      {
          if (fr == lo && to == hi)
              return tree[node];
          
          int m = (lo + hi) / 2;
          if (to <= m) 
              return  query(node * 2, lo, m, fr, to);
          else if (fr > m)
              return query(node * 2 + 1, m + 1, hi, fr, to);
          
          int lid = query(node * 2, lo, m, fr, m);
          int rid = query(node * 2 + 1, m + 1, hi, m + 1, to);
          return a[lid] >= a[rid] ? lid : rid;
      }
      
      
  }
  
  
  private long inv(long v)
  {
      return pow(v, MOD-2);
  }
  
  private long pow(long v, long p)
  {
      long ans = 1;
      while (p > 0)
      {
          if (p % 2 == 1)
              ans = ans * v % MOD;
          v = v * v % MOD;
          p = p / 2;
      }
      return ans;
  }
  
  private double dist(double x, double y, double xx, double yy)
  {
      return Math.sqrt((xx - x) * (xx - x) + (yy - y) * (yy - y));
  }
  

  
 
  private int mod_add(int a, int b) {
      int v = a + b;
      if (v >= MOD) v -= MOD;
      return v;
  }
  
  
  private long overlap(int x1, int y1, int x2, int y2, int x3, int y3, int x4, int y4) {
      if (x1 > x3) return overlap(x3, y3, x4, y4, x1, y1, x2, y2);
      
      if (x3 > x2 || y4 < y1 || y3 > y2) return 0L;
      
      //(x3, ?, x2, ?)
      int yL = Math.max(y1, y3);
      int yH = Math.min(y2, y4); 
      int xH = Math.min(x2, x4);
      
      return f(x3, yL, xH, yH);
  }
  //return #black cells in rectangle
  private long f(int x1, int y1, int x2, int y2) {
      long dx = 1L + x2 - x1;
      long dy = 1L + y2 - y1;
      if (dx % 2 == 0 || dy % 2 == 0 || (x1 + y1) % 2 == 0) 
          return 1L * dx * dy / 2;
      return 1L * dx * dy / 2 + 1;
  }
  
  private int distM(int x, int y, int xx, int yy) {
      return abs(x - xx) + abs(y - yy);
  }
  
  private boolean less(int x, int y, int xx, int yy) {
      return x < xx || y > yy;
  }
  
  private int mul(int x, int y) {
      return (int)(1L * x * y % MOD);
  }
  
  
 
  
  private int nBit1(int v) {
      int v0 = v;
      int c = 0;
      while (v != 0) {
          ++c;
          v = v & (v - 1);
      }
      return c;
  }
  
  private long abs(long v) {
      return v > 0 ? v : -v;
  }
  
  private int abs(int v) {
      return v > 0 ? v : -v;
  }
  
  private int common(int v) {
      int c = 0;
      while (v != 1) {
          v = (v >>> 1);
          ++c;
      }
      
      return c;
  }
  
  private void reverse(char[] a, int i, int j) {
      while (i < j) {
          swap(a, i++, j--);
      }
  }
  
  private void swap(char[] a, int i, int j) {
      char t = a[i];
      a[i] = a[j];
      a[j] = t;
  }
  
  private int gcd(int x, int y) {
      if (y == 0) return x;
      return gcd(y, x % y);
  }
  private long gcd(long x, long y) {
      if (y == 0) return x;
      return gcd(y, x % y);
  }
  private int max(int a, int b) {
      return a >  b ? a : b;
  }
  
  private long max(long a, long b) {
      return a >  b ? a : b;
  }
  
  private int min(int a, int b) {
      return a >  b ? b : a;
  }
  
  private long min(long a, long b) {
      return a >  b ? b : a;
  }
  
  static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;
 
        public FastReader(BufferedReader in)
        {            
            br = in;
        }
 
        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    String line = br.readLine();
                    if (line == null || line.length() == 0) return "";
                    st = new StringTokenizer(line);
                }
                catch (IOException  e)
                {
                    return "";
                    //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)
            {
                return null;
                //e.printStackTrace();
            }
            return str;
        }
    }
}