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.
from time import*
n=int(input())
t=time()
p2=1
v=0
while p2*2<=n:
    p2*=2
    v+=1
mo=10**9+7
tr=[n//(2**k) for k in range(v+1)]
tabn=[0]*(v+1)
tabn[-2]=tr[-2]-1
for k in range(2,n):
    if tr[v-1]<k-2:
        v-=1
    tab=tabn[:]
    tabn=[0]*(v+1)
    for j in range(v):
        tabn[j]=(max((tr[j]-k),0)*tab[j]+(tr[j]-tr[j+1])*tab[j+1])%mo
s=tabn[0]
p2=1
v=0
while p2*2<=n:
    p2*=2
    v+=1
tr=[n//(3*2**k) for k in range(v+1)]
tr3=[n//(2**k) for k in range(v+1)]
tab3n=[0]*(v+1)
tabn=[0]*(v+1)
tabn[-2]=tr[-2]#3*2**k-1
for k in range(1,n):
    if tr3[v-1]<k-2:
        v-=1
    tab=tabn[:]
    tabn=[0]*(v+1)
    tab3=tab3n[:]
    tab3n=[0]*(v+1)
    for j in range(v):
        tabn[j]=(max((tr[j]-k),0)*tab[j]+(tr[j]-tr[j+1])*tab[j+1])%mo
    for j in range(v):
        tab3n[j]=(max((tr3[j]-k),0)*tab3[j]+(tr3[j]-tr3[j+1])*tab3[j+1]+(tr3[j]-tr[j])*tab[j])%mo
print((s+tab3n[0])%mo)
