A permutation of length n is an array consisting of n distinct integers from 1 to n in arbitrary order. For example, [2,3,1,5,4] is a permutation, but [1,2,2] is not a permutation (2 appears twice in the array) and [1,3,4] is also not a permutation (n=3 but there is 4 in the array).

Consider a permutation p of length n, we build a graph of size n using it as follows: 

  * For every 1 ≤ i ≤ n, find the largest j such that 1 ≤ j < i and p_j > p_i, and add an undirected edge between node i and node j 
  * For every 1 ≤ i ≤ n, find the smallest j such that i < j ≤ n and p_j > p_i, and add an undirected edge between node i and node j 



In cases where no such j exists, we make no edges. Also, note that we make edges between the corresponding indices, not the values at those indices.

For clarity, consider as an example n = 4, and p = [3,1,4,2]; here, the edges of the graph are (1,3),(2,1),(2,3),(4,3).

A permutation p is cyclic if the graph built using p has at least one simple cycle. 

Given n, find the number of cyclic permutations of length n. Since the number may be very large, output it modulo 10^9+7.

Please refer to the Notes section for the formal definition of a simple cycle

Input

The first and only line contains a single integer n (3 ≤ n ≤ 10^6).

Output

Output a single integer 0 ≤ x < 10^9+7, the number of cyclic permutations of length n modulo 10^9+7.

Examples

Input


4


Output


16

Input


583291


Output


135712853

Note

There are 16 cyclic permutations for n = 4. [4,2,1,3] is one such permutation, having a cycle of length four: 4 → 3 → 2 → 1 → 4.

Nodes v_1, v_2, …, v_k form a simple cycle if the following conditions hold: 

  * k ≥ 3. 
  * v_i ≠ v_j for any pair of indices i and j. (1 ≤ i < j ≤ k) 
  * v_i and v_{i+1} share an edge for all i (1 ≤ i < k), and v_1 and v_k share an edge. 
# A = "b"
# B = ["aabbb"]
# dic = {}
# for i in B:
# 	dic[i] = 1
# ans = []
# def fun(start, n,ans, v, length):
# 	if length==n:
# 		ans+=[v[:-1]]
# 	for i in range(start, n):
# 		for j in range(start+1,n+1):
# 			try:
# 				if dic[A[i:j]]==1:
# 					fun(j,n,ans,v+A[i:j]+' ', length+len(A[i:j]))
# 			except:
# 				continue
# fun(0,len(A),ans, '', 0)
# ans.sort()


#Question 3
# arr = [1,1,2]
# n = int(input())
# ans = 1
# for i in range(1,n-1):
# 	x = n-i-1
# 	t = x*(x+1)//2
# 	if i-1>0:
# 		t*=(i-1)
# 	ans+= t%(10**9 +7)
# print(ans%(10**9 +7))
n = int(input())
f = 1
for i in range(2,n+1):
	f = f*i
	f%=(10**9 + 7)
p = pow(2,n-1,10**9 +7)
print((f-p)%(10**9 +7))