Count Distinct Structurally Unique Balanced Prime Binary Trees

We define a Balanced Prime Binary Tree in a very specific way: a tree that uses N prime numbers is considered valid if and only if N is of the form (2^k - 1) for some positive integer (k). In other words, the given number (N) should satisfy (N + 1 = 2^k) where (k \ge 1). If (N) is of this form, there exists exactly one unique structure; otherwise, no such balanced tree can be formed.

Return the answer modulo (10^9+7).

inputFormat

The input consists of a single line containing an integer (N) ((1 \leq N \leq 10^9)) representing the number of prime numbers available.

outputFormat

Output a single integer which is the number of structurally unique balanced prime binary trees that can be formed with (N) prime numbers, taken modulo (10^9+7).## sample

3

1