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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;

/**
 * @author Don Li
 */
public class Squares {
    void solve() {
        // let f(n,m) = the number of squares in a n x m table, then f(n,m) = ∑(n-i)(m-i) where 0≤i<min(n,m)
        long x = in.nextLong();

        List<Long> N = new ArrayList<>(), M = new ArrayList<>();

        // a = ∑i, b = ∑i(i-1)
        long a = 0, b = 0;

        // let n≤m, enum all n = 1,2,... (which iterate at most O(n^-3) times) and calc values for m = (x-b)/a + n-1
        for (long n = 1; ; n++) {
            a += n;
            b += n * (n - 1);
            if (x - b <= 0) break;
            if ((x - b) % a == 0) {
                long m = (x - b) / a + n - 1;
                N.add(n);
                M.add(m);
            }
        }

        int last = N.size() - 1;
        if (N.get(last).equals(M.get(last))) last--;
        for (int i = last; i >= 0; i--) {
            N.add(M.get(i));
            M.add(N.get(i));
        }
        out.println(N.size());
        for (int i = 0; i < N.size(); i++) {
            out.printf("%d %d%n", N.get(i), M.get(i));
        }
    }

    public static void main(String[] args) {
        in = new FastScanner(new BufferedReader(new InputStreamReader(System.in)));
        out = new PrintWriter(System.out);
        new Squares().solve();
        out.close();
    }

    static FastScanner in;
    static PrintWriter out;

    static class FastScanner {
        BufferedReader in;
        StringTokenizer st;

        public FastScanner(BufferedReader in) {
            this.in = in;
        }

        public String nextToken() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(in.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

        public double nextDouble() {
            return Double.parseDouble(nextToken());
        }
    }
}