write a go solution for Description:
Let's define a function f(p) on a permutation p as follows. Let g_i be the greatest common divisor (GCD) of elements p_1, p_2, ..., p_i (in other words, it is the GCD of the prefix of length i). Then f(p) is the number of distinct elements among g_1, g_2, ..., g_n.

Let f_max(n) be the maximum value of f(p) among all permutations p of integers 1, 2, ..., n.

Given an integers n, count the number of permutations p of integers 1, 2, ..., n, such that f(p) is equal to f_max(n). Since the answer may be large, print the remainder of its division by 1000,000,007=10^9+7.

Input Format:
The only line contains the integer n (2<=n<=10^6) — the length of the permutations.

Output Format:
The only line should contain your answer modulo 10^9+7.

Note:
Consider the second example: these are the permutations of length 3:

- [1,2,3], f(p)=1.
- [1,3,2], f(p)=1.
- [2,1,3], f(p)=2.
- [2,3,1], f(p)=2.
- [3,1,2], f(p)=2.
- [3,2,1], f(p)=2.

The maximum value f_max(3)=2, and there are 4 permutations p such that f(p)=2.. Output only the code with no comments, explanation, or additional text.