Single-peak arrangement

"Title description"

An n's full permutation a[i] is a single-peak, when and only if there is an X that makes A[1]<a[2]<...<a[x]>a[x+1]>...>a[n].

For example, for a 9 full arrangement, 125798643 is a single-peak arrangement, and 123456789 is a single-peak arrangement, but 356298741 is not.

Try to find the number of a single peak of N.

"Input Format"

An integer n

"Output Format"

The total number of single-peak permutations.

Because the result can be large, output the result to 1234567 after the modulo.

"Sample Input"

3

"Sample Output"

4

"Data Range"

1<=n<=2000000000

Analysis

First, be clear: n must be the highest point of the "peak", followed by n-1,n-2,...,1. Among them, n-1 this number can be placed on the left of the "mountain", can also be placed on the right of the "mountain", and then n-2 is also so ... Until 1, there are two kinds of placement schemes, so the final result is 2^n-1.

Only know that this is not enough, if the loop to find the time, so the use of fast power or divide the solution, the following code is divided.

var
  n:longint;
function FCT (x:longint): Qword;
Begin
  If X=0 then exit (1);
  If X=1 then exit (2);
  FCT:=SQR (FCT (x Div 2)) mod 1234567;
  If x mod 2<>0 then fct:=fct*2 mod 1234567;
End;
Begin
  Read (n);
  Write (FCT (n-1));
End.