Problem: You are given a positive integer n.

Find a sequence of fractions (a_i)/(b_i), i = 1 … k (where a_i and b_i are positive integers) for some k such that:

$$$ \begin{cases} $b_i$ divides $n$, $1 < b_i < n$ for $i = 1 … k$ \\\ $1 ≤ a_i < b_i$ for $i = 1 … k$ \\\ \text{$∑_{i=1}^k (a_i)/(b_i) = 1 - 1/n$} \end{cases} $$$

Input

The input consists of a single integer n (2 ≤ n ≤ 10^9).

Output

In the first line print "YES" if there exists such a sequence of fractions or "NO" otherwise.

If there exists such a sequence, next lines should contain a description of the sequence in the following format.

The second line should contain integer k (1 ≤ k ≤ 100 000) — the number of elements in the sequence. It is guaranteed that if such a sequence exists, then there exists a sequence of length at most 100 000.

Next k lines should contain fractions of the sequence with two integers a_i and b_i on each line.

Examples

Input


2


Output


NO


Input


6


Output


YES
2
1 2
1 3

Note

In the second example there is a sequence 1/2, 1/3 such that 1/2 + 1/3 = 1 - 1/6.

Solution (in JAVA):

Solution:

import java.io.*;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.*;

public class NewClass {

    static StringBuffer str = new StringBuffer();
    static InputReader in = new InputReader(System.in);
    static int mm = 1000000007;
static void printDivisors(int n) 
    {         
        int fl=-1;
        for (int i=2; i<=Math.sqrt(n); i++) 
        { 
            if (n%i==0) 
            { 
                // If divisors are equal, print only one 
                if (n/i == i) 
                    continue;
       
                else {// Otherwise print both 
                    int a=i;
                    int b=n/i;
                    if(gcdi(a,b)==1)
                    {
                        int x=n/a;
                        int y=n/b;
                        int cc=1;
                        while(x*cc<n-1){
                            int vv=n-1-x*cc;
                            if(vv%y==0){
                                System.out.println("YES");
                                System.out.println(2);
                                System.out.println(cc+" "+a+"\n"+vv/y+" "+b);
                                fl=1;
                                return;
                            }
                            cc++;
                        }
                    }
                }
            } 
        }
        if(fl==-1)
            System.out.println("NO");
    } 
    public static void main(String[] args) {
        int t, i, j, tt, m, n, k;
        n=in.nextInt();
        printDivisors(n) ;
    }
    static final Comparator<Entity> com = new Comparator<Entity>() {
        public int compare(Entity x, Entity y) {
            int xx = Long.compare(y.a, x.a);
            if (xx == 0) {
                return Long.compare(x.b, y.b);
            } else {
                return xx;
            }
        }
    };

    static class Entity {

        long a;
        long b;

        Entity(long p, long q) {
            a = p;
            b = q;
        }
    }

    static long gcd(long a, long b) {
        return (b == 0) ? a : gcd(b, a % b);
    }

    static int gcdi(int a, int b) {
        return (b == 0) ? a : gcdi(b, a % b);
    }

    static long power(long x, int y, int m) {
        if (y == 0) {
            return 1;
        }
        long p = power(x, y / 2, m) % m;
        p = (p * p) % m;
        return (y % 2 == 0) ? p : (x * p) % m;
    }

    public static void ap(String st) {
        str.append(st);
    }

    public static void pn() {
        System.out.println(str);
    }

    static class InputReader {

        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

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

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

        public int peek() {
            if (numChars == -1) {
                return -1;
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    return -1;
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar];
        }

        public void skip(int x) {
            while (x-- > 0) {
                read();
            }
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

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

        public String next() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuffer res = new StringBuffer();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));

            return res.toString();
        }

        public String nextLine() {
            StringBuffer buf = new StringBuffer();
            int c = read();
            while (c != '\n' && c != -1) {
                if (c != '\r') {
                    buf.appendCodePoint(c);
                }
                c = read();
            }
            return buf.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 boolean hasNext() {
            int value;
            while (isSpaceChar(value = peek()) && value != -1) {
                read();
            }
            return value != -1;
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
    }
}