human
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. 
The above is tricky. Write me a correct solution in PYTHON3.

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Give me a Python code to 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?
assistant
#Here is Python code to 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 
.

n = int(input().strip())
mod = 10**9+7
# import sys
# # sys.setrecursionlimit(10**9)
# def power(num):
#     if num==1: return 1
#     else: return (power(num-1)*2)%mod

# def fac(num):
#     if num==1: return 1
#     else: return (fac(num-1)*num)%mod
# n=583291
power = 1
fac = 1
for i in range(2, n+1):
    power = (power*2)%mod
    fac = (fac*i)%mod
print((fac-power)%mod)

# print([fac(n)-power(n) for n in [1,2,3,4,583291]])
# print(power(583291))
# print(fac(583291))
# print()