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.
 What is 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 
.

import os

from collections import defaultdict, deque

is_dev = 'vscode' in os.environ

if is_dev:
    inF = open('in.txt', 'r')
    outF = open('out.txt', 'w')

def ins():
    return list(map(int, input_().split(' ')))

def inss():
    return list(input_().split(' '))

def input_():
    if is_dev:
        return inF.readline()[:-1]
    else:
        return input()
    
def ranin():
    return range(int(input_()))

def print_(data):
    if is_dev:
        outF.write(str(data)+'\n')
    else:
        print(data)

k = 1e9 + 7
n = int(input_())

x = 1
for i in range(1,n+1):
    x *= i
    x = int(x % k)

j = 1
for i in range(n-1):
    j *= 2
    j %= k
    
if x <= j:
    print_(int((k + x) - j))
else:
    print_(int(x - j))
    
if is_dev:
    outF.close()
    def compare_file():
        print(open('out.txt', 'r').read() == open('outactual.txt', 'r').read())
    compare_file()