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;

public class SpongeBobAndSquares {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);

        long nSquares = Long.parseLong(br.readLine());
        ArrayList<Grid> grids = new ArrayList<>();
        grids.add(new Grid(1, nSquares));
        long n = 2, m = nSquares - 1;
        while (true) {
            if (n > m) {
                break;
            }
            m = getM(nSquares, n + 1, m + 1);
            if (m > -1) {
                grids.add(new Grid(n, m - 1));
            }

            n++;
            m = Math.abs(m) - 1;
        }

        for (int i = grids.size() - 1; i > -1; i--) {
            Grid grid = grids.get(i);
            if (grid.m != grid.n) {
                grids.add(new Grid(grid.m, grid.n));
            }
        }
        int l = grids.size();
        out.println(l);
        for (int i = 0; i < l; i++) {
            out.println(grids.get(i).n + " " + grids.get(i).m);
        }
        out.close();
    }

    private static long getM(long nSquares, long n, long m) {
        long l = n - 1, r = m + 1;
        while (r - l > 1) {
            long mid = (l + r) / 2;
            long squares = countSquares(n - 1, n, mid);
            if (squares == nSquares) {
                return mid;
            }
            if (squares > nSquares) {
                r = mid;
            } else {
                l = mid;
            }
        }
        return r * -1L;
    }

    private static long countSquares(long i, long n, long m) {
        long sigmaI2 = (i * (i + 1) * (2 * i + 1)) / 6;
        long sigmaI = (i * (i + 1)) / 2;
        long sigmaOne = i;
        if (sigmaI2 < 0 || sigmaI < 0 || (n + m) * sigmaI < 0 || n * m * sigmaOne < 0) {
            System.exit(-1);
        }
        return sigmaI2 - (n + m) * sigmaI + n * m * sigmaOne;
    }

    private static class Grid {
        public long n;
        public long m;

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