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.util.Scanner;

public class SpongebobAndSquares {
  
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    long x = sc.nextLong();
    long weight[] = new long[1 << 23]; // max number of w and l pair possible (derived from formula in workbook)
    long length[] = new long[1 << 23];
    
    long w = 1;
    int i = 0;
    while (isInRange(w, x)) {
      long l = getLength(w,x);
      if (l > 0) {
        weight[i] = w;
        length[i] = l;
        i++;
      }
      w++;
    }
    
    int k = 0;
    for (i = 0; weight[i] > 0; i++) {
      if (weight[i] != length[i])
        k+=2;
      else
        k++;
    }
    int lastIdx = i-1;
    
    System.out.println(k);
    for (i = 0; weight[i] > 0; i++) {
      System.out.println(weight[i] + " " + length[i]);
    }
    
    for (i = lastIdx; i >= 0; i--) {
      if (weight[i] != length[i]) {
        System.out.println(length[i] + " " + weight[i]);
      }
    }
  }
  
  /*
   * See programming workbook for derivation of the range condition
   */
  public static boolean isInRange(long w, long x) {
    long left = (2 * w*w*w) + (3 * w*w) + w;
    long right = 6 * x;
    return left <= right;
  }
  
  public static long getLength(long w, long x) {
    long nominator = (6 * x) + (w*w*w) - w;
    long denominator = (3 * w*w) + (3 * w);
    return (nominator % denominator) == 0 ? (nominator/denominator) : -1;
  }
  
}