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:
/*
Keep solving problems. 
*/

import java.util.*;
import java.io.*;

public class CFA {

    BufferedReader br;
    PrintWriter out;
    StringTokenizer st;
    boolean eof;
    final long MOD = 1000L * 1000L * 1000L * 2 + 10;
    int[] dx = {-1, 1, 0, 0};
    int[] dy = {0, 0, -1, 1};

    class Node implements Comparable<Node> {
        long x;
        long y;

        public Node(long x, long y) {
            this.x = x;
            this.y = y;
        }
        @Override
        public int compareTo(Node o) {
            if (this.x != o.x) {
                return this.x < o.x ? -1 : 1;
            }
            return this.y < o.y ? -1 : 1;
        }
    }
    void solve() throws IOException {
        long x = nextLong();
        List<Long> resx = new ArrayList<>();
        List<Long> resy = new ArrayList<>();
        for (long n = 1; n * n * n < 6 * x; n++) {
            long total = 6 * x + n * n * n - n;
            if (total % (3 * n * n + 3 * n) == 0) {
                long m = total / 3 / n / (n + 1);
                if (m > n) {
                    resx.add(n);
                    resy.add(m);
                    resx.add(m);
                    resy.add(n);
                }
                else if (m == n) {
                    resx.add(n);
                    resy.add(n);
                }
            }
        }

        Node[] arr = new Node[resx.size()];
        for (int i = 0; i < arr.length; i++) {
            arr[i] = new Node(resx.get(i), resy.get(i));
        }
        Arrays.sort(arr);

        outln(resx.size());
        for (int i = 0; i < resx.size(); i++) {
            outln(arr[i].x + " " + arr[i].y);
        }
    }

    void shuffle(int[] a) {
        int n = a.length;
        for(int i = 0; i < n; i++) {
            int r = i + (int) (Math.random() * (n - i));
            int tmp = a[i];
            a[i] = a[r];
            a[r] = tmp;
        }
    }

    private void outln(Object o) {
        out.println(o);
    }
    private void out(Object o) {
        out.print(o);
    }
    public CFA() throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        solve();
        out.close();
    }
    public static void main(String[] args) throws IOException {
        new CFA();
    }

    public long[] nextLongArr(int n) throws IOException{
        long[] res = new long[n];
        for(int i = 0; i < n; i++)
            res[i] = nextLong();
        return res;
    }
    public int[] nextIntArr(int n) throws IOException {
        int[] res = new int[n];
        for(int i = 0; i < n; i++)
            res[i] = nextInt();
        return res;
    }
    public String nextToken() {
        while (st == null || !st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                eof = true;
                return null;
            }
        }
        return st.nextToken();
    }
    public String nextString() {
        try {
            return br.readLine();
        } catch (IOException e) {
            eof = true;
            return null;
        }
    }
    public int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }
    public long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }
    public double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }
}