A × B × C

2.0s 256M

You are given a positive integer \(K\). Count the number of ordered triples \((A, B, C)\) satisfying \(A \times B \times C \le K\).

The triples are ordered, so for example \((1,1,2)\) and \((1,2,1)\) are considered different triples.

Input

The input consists of a single line containing the integer \(K\).

Constraints

  • \(1 \le K \le 10^{7}\)

Output

Output a single integer equal to the desired count.

Scoring

There are two subtasks. Each subtask contains multiple test cases, and you earn the subtask's score only if you solve all of its tests.

  • Subtask \(1\) (1 point): \(K \le 500\).
  • Subtask \(2\) (2 points): no additional constraints.

Sample Input 1

2

Sample Output 1

4

Sample Input 2

10

Sample Output 2

53

Sample Input 3

10000000

Sample Output 3

1421760251

Source

This task is adapted from AtCoder Regular Contest 113 A - A*B*C, with adjusted constraints.

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