Problem: Spongebob is already tired trying to reason his weird actions and calculations, so he simply asked you to find all pairs of n and m, such that there are exactly x distinct squares in the table consisting of n rows and m columns. For example, in a 3 × 5 table there are 15 squares with side one, 8 squares with side two and 3 squares with side three. The total number of distinct squares in a 3 × 5 table is 15 + 8 + 3 = 26.

Input

The first line of the input contains a single integer x (1 ≤ x ≤ 1018) — the number of squares inside the tables Spongebob is interested in.

Output

First print a single integer k — the number of tables with exactly x distinct squares inside.

Then print k pairs of integers describing the tables. Print the pairs in the order of increasing n, and in case of equality — in the order of increasing m.

Examples

Input

26


Output

6
1 26
2 9
3 5
5 3
9 2
26 1


Input

2


Output

2
1 2
2 1


Input

8


Output

4
1 8
2 3
3 2
8 1

Note

In a 1 × 2 table there are 2 1 × 1 squares. So, 2 distinct squares in total.

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In a 2 × 3 table there are 6 1 × 1 squares and 2 2 × 2 squares. That is equal to 8 squares in total.

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Solution (in JAVA):

Solution:
import java.io.*;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.*;

public class Template implements Runnable {

    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok = new StringTokenizer("");

    void init() throws FileNotFoundException {
        try {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        } catch (Exception e) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        }
    }

    String readString() throws IOException {
        while (!tok.hasMoreTokens()) {
            try {
                tok = new StringTokenizer(in.readLine(), " :");
            } catch (Exception e) {
                return null;
            }
        }
        return tok.nextToken();
    }

    int readInt() throws IOException {
        return Integer.parseInt(readString());
    }

    int[] readIntArray(int size) throws IOException {
        int[] res = new int[size];
        for (int i = 0; i < size; i++) {
            res[i] = readInt();
        }
        return res;
    }

    long readLong() throws IOException {
        return Long.parseLong(readString());
    }

    double readDouble() throws IOException {
        return Double.parseDouble(readString());
    }

    <T> List<T>[] createGraphList(int size) {
        List<T>[] list = new List[size];
        for (int i = 0; i < size; i++) {
            list[i] = new ArrayList<>();
        }
        return list;
    }

    public static void main(String[] args) {
        new Thread(null, new Template(), "", 1l * 200 * 1024 * 1024).start();
    }

    long timeBegin, timeEnd;

    void time() {
        timeEnd = System.currentTimeMillis();
        System.err.println("Time = " + (timeEnd - timeBegin));
    }

    long memoryTotal, memoryFree;

    void memory() {
        memoryFree = Runtime.getRuntime().freeMemory();
        System.err.println("Memory = " + ((memoryTotal - memoryFree) >> 10)
                + " KB");
    }

    public void run() {
        try {
            timeBegin = System.currentTimeMillis();
            memoryTotal = Runtime.getRuntime().freeMemory();
            init();
            solve();
            out.close();
            if (System.getProperty("ONLINE_JUDGE") == null) {
                time();
                memory();
            }
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(-1);
        }
    }

    long cntSq(int x, int y) {
        int ans = 0;
        for (int size = 1; size <= Math.min(x, y); size++) {
            for (int i = 0; i < x; i++) {
                for (int j = 0; j < y; j++) {
                    if (i + size <= x && j + size <= y) ans++;
                }
            }
        }
        return ans;
    }

    class P implements Comparable<P> {
        long n;
        long m;

        public P(long n, long m) {
            this.n = n;
            this.m = m;
        }

        @Override
        public int compareTo(P o) {
            if (n != o.n) return Long.compare(n, o.n);
            return Long.compare(m, o.m);
        }
    }

    void solve() throws IOException {
        long size = readLong();
        long prev = 0;
        long prevDiff = 0;
        List<P> answer = new ArrayList<>();
        for (int i = 1; ; i++) {
            prev += (long) i * i;
            prevDiff += i;
            if (prev == size) {
                answer.add(new P(i, i));
            }
            if (prev >= size) break;
            long diff = size - prev;
            if (diff % prevDiff == 0) {
                long cnt = diff / prevDiff;
                long other = i + cnt;
                answer.add(new P(i, other));
                answer.add(new P(other, i));
            }
        }
        Collections.sort(answer);
        out.println(answer.size());
        for (P p : answer) {
            out.println(p.n + " " + p.m);
        }

//        for (int w = 1; w <= 10; w++) {
//            for (int h = w; h <= 10; h++) {
//                System.err.println(w + "x" + h + ": " + cntSq(w, h));
//            }
//        }
    }


}