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

import os
import sys
from io import BytesIO, IOBase

_str = str
BUFSIZE = 8192


def str(x=b''):
    return x if type(x) is bytes else _str(x).encode()


class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = 'x' in file.mode or 'r' not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b'\n') + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode('ascii'))
        self.read = lambda: self.buffer.read().decode('ascii')
        self.readline = lambda: self.buffer.readline().decode('ascii')


def inp():
    return sys.stdin.readline().rstrip()


def mpint():
    return map(int, inp().split(' '))


def itg():
    return int(inp())


# ############################## import
# from ACgenerator.Y_Testing import get_code
MOD = int(1e9) + 7
MAXSIZE = int(1e6) + 3
STACK = {}


def cache(func):
    STACK[func.__name__] = []

    def new_func(n):
        stack = STACK[func.__name__]
        while n >= len(stack):
            stack.append(func(len(stack)))
        return stack[n]

    return new_func


@cache
def A000142(n):
    """
    Factorial numbers: n! = 1*2*3*4*...*n
    1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600, 6227020800,

    O(n): a(n)
    O(n): a(0)~a(n)

    Cited by:
    A059204 (number of permutations of n letters)
    """
    return 1 if n <= 1 else (A000142(n - 1) * n) % MOD


@cache
def A011782(n):
    """
    2^n
    1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536,

    O(logn): a(n) ( using builtin pow )
    O(n): a(0)~a(n)

    Cited by:
    A059204:
    number of unimodal permutations e.g. 12345 or 54321 or 12543
    permutations like 213 or 312 are not
    and there are 2^(n-1) that is unimodal which n is the number of items
    """
    return 1 if n <= 0 else (A011782(n - 1) << 1) % MOD


def A059204(n):
    """
    Number of non-unimodal permutations of n items
    (i.e., those which do not simply go up for the first part
    and then down for the rest, but at some point go down then up).
    e.g. 213 or 312 is non-unimodal
    and 12345 or 54321 or 12543 is unimodal

    0, 0, 0, 2, 16, 104, 688, 4976, 40192, 362624, 3628288, 39915776, 478999552, 6227016704

    O(n): a(n)
    O(n): a(0)~a(n)
    """
    return (A000142(n) - A011782(n - 1)) % MOD


# ############################## main
def solve():
    return A059204(itg())


def main():
    # print("YES" if solve() else "NO")
    # print("yes" if solve() else "no")
    # solve()
    print(solve())
    # for _ in range(itg()):
    #     print(solve())


DEBUG = 0
URL = 'https://codeforces.com/contest/1391/problem/C'

if __name__ == '__main__':
    if DEBUG == 1:
        import requests  # ImportError: cannot import name 'md5' from 'sys' (unknown location)
        from ACgenerator.Y_Test_Case_Runner import TestCaseRunner

        runner = TestCaseRunner(main, URL)
        inp = runner.input_stream
        print = runner.output_stream
        runner.checking()
    elif DEBUG == 2:
        main()
    else:
        sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
        main()
# Please check!
