Problem H
Three in a Row
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The mathematician Lenore Oljer has done so much math that she has grown tired of prime numbers. She has now started studying so-called “nice triplets”. It’s very easy to create a nice triplet. Start with an integer $a$ greater than zero and then create the triplet $(a, a+1, a+2)$. All triplets created in this way are considered nice. Some examples of nice triplets are $(4,5,6)$ and $(15,16,17)$.
To learn more about nice triplets, Lenore wants to find out how many numbers can be written as the product of all the numbers in a nice triplet. She calls these numbers “triple numbers”. Some examples of triple numbers are $24=2 \cdot 3 \cdot 4$ and $336 = 6 \cdot 7 \cdot 8$. Lenore now wants to know how many triple numbers there are that are less than the given number $N$.
Write a program that takes the number $N$ as input and prints out how many numbers less than $N$ that are triple numbers.
Input
The first and only line of the input contains the integer $N$ ($1 \le N \le 10^9$), whose meaning is described above.
Output
Print an integer: the number of integers less than $N$ that are triple numbers.
Points
Your solution will be tested on several test case groups. To get the points for a group, it must pass all the test cases in the group.
|
Group |
Point value |
Constraints |
|
$1$ |
$20$ |
$N \leq 30$ |
|
$2$ |
$20$ |
$N \leq 80$ |
|
$3$ |
$20$ |
$N \leq 1000$ |
|
$4$ |
$20$ |
$N \leq 10^5$ |
|
$5$ |
$20$ |
No additional constraints. |
| Sample Input 1 | Sample Output 1 |
|---|---|
30 |
2 |
| Sample Input 2 | Sample Output 2 |
|---|---|
24 |
1 |
| Sample Input 3 | Sample Output 3 |
|---|---|
1234 |
9 |
