Given an integer $N$, count the number of pairs $(a, b)$ that satisfy the following conditions:

1. $1 \leq a < b \leq N$
2. $a + b$ divides $a \times b$

Input Format

A single line containing the integer $N$.

Output Format

A single line containing an integer representing the number of pairs $(a, b)$ that meet the conditions.

Example

Input:

15

Output:

4

Notes

Data scale and conditions:

• $\text{test1: } N \leq 5 \times 10^7$
• $\text{test2: } N \leq 10^8$
• $\text{test3: } N \leq 2 \times 10^8$
• $\text{test4: } N \leq 3 \times 10^8$
• $\text{test5: } N \leq 5 \times 10^8$
• $\text{test6: } N \leq 10^9$
• $\text{test7: } N \leq 10^9$
• $\text{test8: } N \leq 2^{31}-1$
• $\text{test9: } N \leq 2^{31}-1$
• $\text{test10: } N \leq 2^{31}-1$