Problem: Iahub wants to enhance his multitasking abilities. In order to do this, he wants to sort n arrays simultaneously, each array consisting of m integers.

Iahub can choose a pair of distinct indices i and j (1 ≤ i, j ≤ m, i ≠ j). Then in each array the values at positions i and j are swapped only if the value at position i is strictly greater than the value at position j.

Iahub wants to find an array of pairs of distinct indices that, chosen in order, sort all of the n arrays in ascending or descending order (the particular order is given in input). The size of the array can be at most <image> (at most <image> pairs). Help Iahub, find any suitable array.

Input

The first line contains three integers n (1 ≤ n ≤ 1000), m (1 ≤ m ≤ 100) and k. Integer k is 0 if the arrays must be sorted in ascending order, and 1 if the arrays must be sorted in descending order. Each line i of the next n lines contains m integers separated by a space, representing the i-th array. For each element x of the array i, 1 ≤ x ≤ 106 holds.

Output

On the first line of the output print an integer p, the size of the array (p can be at most <image>). Each of the next p lines must contain two distinct integers i and j (1 ≤ i, j ≤ m, i ≠ j), representing the chosen indices.

If there are multiple correct answers, you can print any.

Examples

Input

2 5 0
1 3 2 5 4
1 4 3 2 5


Output

3
2 4
2 3
4 5


Input

3 2 1
1 2
2 3
3 4


Output

1
2 1

Note

Consider the first sample. After the first operation, the arrays become [1, 3, 2, 5, 4] and [1, 2, 3, 4, 5]. After the second operation, the arrays become [1, 2, 3, 5, 4] and [1, 2, 3, 4, 5]. After the third operation they become [1, 2, 3, 4, 5] and [1, 2, 3, 4, 5].

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class CodeForces {
    /*****************************************WRITING CODE STARTS HERE******************************************/

    public static void solve(int t)throws IOException {
        int m = sc.nextInt();
        int n = sc.nextInt();
        int k = sc.nextInt();
        out.println(n*(n-1)/2);
        for(int i=1;i<n;i++){
            for(int j=1;j<=n-i;j++)
                if(k==0)
                    out.println(j+" "+(j+1));
                else  out.println((j+1)+" "+j);
        }

    }



    /*****************************************WRITING CODE ENDS HERE******************************************/

    public static void main(String[] args) throws IOException{
        int testCase = 1;
//        testCase = sc.nextInt();
        for (int i = 1; i <= testCase; i++) solve(i);
        closeIO();

    }
    static FastestReader sc = new FastestReader();              // FASTEST INPUT
    static PrintWriter out = new PrintWriter(System.out);                // FAST OUTPUT


    /**************************************HELPER FUNCTION STARTS HERE ************************************/

    public static int mod = (int) 1e9 + 7;
    public static final int inf_int = (int) 1e9;
    public static final long inf_long = (long) 1e15;

    public static final String YES = "YES";
    public static final String NO = "NO";

    // count the length of a number, time O(1)
    public static int countDigitBase10(long n) {
        if (n == 0) return 0;
        return (int) (1 + Math.log10(n));
    }

    // euclidean algorithm
    public static long gcd(long a, long b) {
        // time O(max (loga ,logb))
        long x = Math.min(a, b);
        long y = Math.max(a, b);
        if (y % x == 0) return x;
        return gcd(y % x, x);
    }

    public static long lcm(long a, long b) {
        // lcm(a,b) * gcd(a,b) = a * b
        return (a / gcd(a, b)) * b;
    }
    // binary exponentiation
    public static long power(long x, long n) {
        // time O(logn)
        long ans = 1;
        while (n > 0) {
            if ((n & 1) == 1) {
                ans *= x;
                ans %= mod;
                n--;
            } else {
                x *= x;
                x %= mod;
                n >>= 1;
            }
        }
        return ans;
    }

    public static long firstDivisor(long n) {
        if (n == 1 || n == 0) return n;
        for (long i = 2; i * i <= n; i++)
            if (n % i == 0) return i;
        return -1;
    }

    public static long max3(long a, long b, long c) {
        return max2(max2(a, b), c);
    }

    public static long max2(long a, long b) {
        return Math.max(a, b);
    }

    public static long min3(long a, long b, long c) {
        return min2(min2(a, b), c);
    }

    public static long min2(long a, long b) {
        return Math.min(a, b);
    }

    public static int max3(int a, int b, int c) {
        return max2(max2(a, b), c);
    }

    public static int max2(int a, int b) {
        return Math.max(a, b);
    }

    public static int min3(int a, int b, int c) {
        return min2(min2(a, b), c);
    }

    public static int min2(int a, int b) {
        return Math.min(a, b);
    }

    /**************************************HELPER FUNCTION ENDS HERE ************************************/

    /*****************************************FAST INPUT STARTS HERE *************************************/


    public static void closeIO() throws IOException{
            out.flush();
            out.close();
            sc.close();
    }
    private static class FastestReader {
        private static final int BUFFER_SIZE = 1 << 16;
        private final DataInputStream din;
        private final byte[] buffer;
        private int bufferPointer, bytesRead;

        public FastestReader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public FastestReader(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        private static boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }

        private int skip() throws IOException {
            int b;
            //noinspection StatementWithEmptyBody
            while ((b = read()) != -1 && isSpaceChar(b)) {}
            return b;
        }

        public String next() throws IOException {
            int b = skip();
            final StringBuilder sb = new StringBuilder();
            while (!isSpaceChar(b)) { // when nextLine, (isSpaceChar(b) && b != ' ')
                sb.appendCodePoint(b);
                b = read();
            }
            return sb.toString();
        }

        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ') {
                c = read();
            }
            final boolean neg = c == '-';
            if (neg) { c = read(); }
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (neg) { return -ret; }
            return ret;
        }

        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ') { c = read(); }
            final boolean neg = c == '-';
            if (neg) { c = read(); }
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg) { return -ret; }
            return ret;
        }

        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ') { c = read(); }
            final boolean neg = c == '-';
            if (neg) { c = read(); }

            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg) { return -ret; }
            return ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1) { buffer[0] = -1; }
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead) { fillBuffer(); }
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            din.close();
        }

    }
    /*****************************************FAST INPUT ENDS HERE *************************************/
}