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. 
66
 652615
 482331
 336161
 33
 1000000
 79531
 768208
 3
 885131

257415584
 960319213
 722928541
 234634596
 762187807
 23581336
 162141608
 635322133
 2
 329995454

from sys import stdin, stdout, setrecursionlimit
import threading

# tail-recursion optimization
# In case of tail-recusion optimized code, have to use python compiler.
# Otherwise, memory limit may exceed.
# declare the class class Tail_Recursion_Optimization
class Tail_Recursion_Optimization:
    def __init__(self, recursion_limit, stack_size):
        setrecursionlimit(recursion_limit)
        threading.stack_size(stack_size)
        return None
        
class SOLVE:
    mod = 10**9 + 7
        
    def twon(self, n):
        if n == 0:
            return 1
        
        x = self.twon(n//2)
        if n%2:
            return (2*x**2) % self.mod
        else:
            return (x**2) % self.mod
    
    def solve(self):
        R = stdin.readline
        f = open('input.txt');R = f.readline
        W = stdout.write
        
        n = int(R())
        
        fact_n = 1
        for i in range(2, n+1):
            fact_n *= i
            fact_n %= self.mod
        
        two_n  = self.twon(n-1)
        
        W('%d\n' % (fact_n-two_n + self.mod*(fact_n<two_n)))
        
        return 0
        
def main():
    s = SOLVE()
    s.solve()
#Tail_Recursion_Optimization(10**7, 2**18)
threading.Thread(target=main).start()