Problem Background

It's not so much a sense of reluctance, what even is this chart...
——ReMiRiA
Although winning the championship is very happy, what even is this chart? Will it really be included??
——yoshiki

Problem Description

Fusu enjoys splitting natural numbers.

For a given positive integer \( n \), if \( n = i \times j \times k \), where \( i, j, k \) are positive integers, then the triplet \( (i, j, k) \) is called an excellent split of \( n \).

The triplet \( (i, j, k) \) is ordered. For example, for \( 2 = 1 \times 1 \times 2 = 1 \times 2 \times 1 = 2 \times 1 \times 1 \), we consider \( (1, 1, 2) \), \( (1, 2, 1) \), and \( (2, 1, 1) \) as three different excellent splits.

Now, Fusu wants to know, for \( n = 1, 2, 3 \ldots N \), what is the sum of all excellent splits of \( n \).

Formally, let \( f(n) \) denote the number of excellent splits of \( n \). You need to find \( \sum_{i = 1}^N f(i) \).

Input Format

The input consists of a single line containing an integer \( N \) (\( 1 \leq N \leq 10^{10} \)).

Output Format

Output a single integer representing the answer. Since the answer may be very large, you only need to output the remainder of this value divided by \( 2^{64} \).

Sample Input and Output

Sample Input #1

2

Sample Output #1

4

Sample Input #2

100

Sample Output #2

1471

见题面 Input 部分

见题面 Output 部分