Let's define a function f(p) on a permutation p as follows. Let g_i be the [greatest common divisor (GCD)](https://en.wikipedia.org/wiki/Greatest_common_divisor) 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

The only line contains the integer n (2 ≤ n ≤ 10^6) — the length of the permutations.

Output

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

Examples

Input


2


Output


1

Input


3


Output


4

Input


6


Output


120

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.
def perm(a,b):
    ret = 1
    for i in range(a, a - b, -1):
        ret = (ret * i)%1000000007
    return ret

num = int(input())
num2 = num
c = 0
while num2:
    c += 1
    num2 >>= 1
pow2 = 1 << (c-1)
array = [pow2]
for i in range(c-1):
    array.append(array[-1]>>1)

def calc(arr):
    data = []
    #sm = 0
    av = num
    for i in range(c):
        data.append((num // arr[i] - (num - av), av))
        av -= data[-1][0]


    #print(data)

    ans = 1
    for d in data:
        ans = (ans * (d[0] * perm(d[1] - 1, d[0] - 1)))%1000000007
    return ans

answer = calc(array)

if num >= pow2 // 2 * 3:
    for i in range(1,c):
        dat = [1]
        for j in range(1, c):
            if j == i:
                dat = [3*dat[0]] + dat
            else:
                dat = [2*dat[0]] + dat
        #print(dat)
        a = calc(dat)
        answer += a

print(answer%1000000007)

