CCO Preparation Test 2 - Subsets

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Points: 25 (partial)
Time limit: 0.6s
Memory limit: 128M

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Ada, Assembly, Awk, Brain****, C, C#, C++, COBOL, CommonLisp, D, Dart, F#, Forth, Fortran, Go, Groovy, Haskell, Intercal, Java, JS, Kotlin, Lisp, Lua, Nim, ObjC, OCaml, Octave, Pascal, Perl, PHP, Pike, Prolog, Python, Racket, Ruby, Rust, Scala, Scheme, Sed, Swift, TCL, Text, Turing, VB, Zig

When Bruce learned set theory, he assigned a homework question to his students.

Given a positive integer N, find the number of subsets of the whole set \{1, 2, \dots, N\} that satisfies the following constraint: if an integer x is in the subset, then the integers 2x and 3x are not in the subset. For example, given N = 4, the whole set is \{1, 2, 3, 4\}. The number of subsets satisfying the constraint is 8, including the empty set: \emptyset, \{1\}, \{1, 4\}, \{2\}, \{2, 3\}, \{3\}, \{3, 4\}, and \{4\}.

Input Specification

The input will consist of one integer N (1 \le N \le 100\,000).

Output Specification

Output the number of subsets that satisfy the above constraints mod 1\,000\,000\,001 (= 10^9+1).

Sample Input

4

Sample Output

8

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