BZOJ2734[HNOI2012] Collection of selected

Description

"Set theory and Graph theory" This course has a homework problem, ask the students to find {1, 2, 3, 4, 5} All meet the following conditions of the subset: If X is in this subset, 2x and 3x cannot be in the sub-set. The students do not like the problem with the enumeration nature, so it becomes the following question: For any positive integer n≤100000, how to find out {1, 2,..., n} The number of the subset of the constraints to meet the above constraint (just output the results of 1,000,000,001 modulo), Now this problem is yours.

Input

Only one row, where there is a positive integer n,30% the data satisfies n≤20.

Output

Contains only a positive integer representing the number of subsets of {1, 2,..., n} that meet the above constraints.

Sample Input4Sample Output8
"Sample Interpretation"
There are 8 sets that meet the requirements, namely the empty set, {1},{1,4},{2},{2,3},{3},{3,4},{4}. The following:set X to a number that does not contain 2 and 3 factors, you can construct a matrix like this:

X	X*3	X*3^2	X*3^3	.	.	.
2*x	2*x*3	2*x*3^2	2*x*3^3	.	.	.
2^2*x	2^2*x*3	2^2*x*3^2	2^2*x*3^3	.	.	.
2^3*x	2^3*x*3	2^3*x*3^2	2^3*x*3^3	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.

  For example, when X=1:

1	3	9	27	.	.	.
2	6	18	54	.	.	.
4	12	36	108	.	.	.
8	24	72	216	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.

in this way, the number pairs that cannot be taken at the same time must be around or up or down in the matrix. Because of the n<=1000000, the matrix has a maximum of 11 columns, and each row can be state-compressed DP. each number must and only exist in a matrix, there is no correlation between the two matrices, so the DP out of each matrix of the number of feasible scheme, the last multiplication is possible. Code:

1 Const2mo=1000000001;3 var4 I,j,k,l,n,m:longint;5A:Array[0.. -,0.. -] ofLongint;6B:Array[0.. -] ofLongint;7F:Array[0.. -,0..2048] ofLongint;8BoArray[0..100005] ofLongint;9BinArray[0.. -] ofLongint;Ten Ans:int64; One functionQQ (X:longint): Longint; A varI,j,y:longint; - begin -Fillchar (b,sizeof (b),0); thea[1,1]:=x; -    fori:=2  to  -  Do -   ifa[i-1,1]*2<=n ThenA[i,1]:=a[i-1,1]*2 ElseA[i,1]:=n+1; -    fori:=1  to  -  Do +    forj:=2  to  One  Do -   ifa[i,j-1]*3<=n Thena[i,j]:=a[i,j-1]*3 Elsea[i,j]:=n+1; +    fori:=1  to  -  Do A    forj:=1  to  One  Do at   ifA[i,j]<=n Then -   begin -b[i]:=b[i]+bin[j-1]; -bo[a[i,j]]:=1; -   End; -    fori:=0  to  -  Do in    forj:=0  toB[i] Dof[i,j]:=0; -f[0,0]:=1; to    fori:=0  to  -  Do +    forj:=0  toB[i] Do -   ifF[i,j]>0  Then the    fory:=0  tob[i+1] Do *   if(j andy=0) and(Y and(Y shr1)=0) Thenf[i+1, y]:= (f[i+1, Y]+f[i,j])MoDmo; $Exit (f[ -,0]);Panax Notoginseng End; - begin thebin[0]:=1; +    fori:=1  to  -  Dobin[i]:=bin[i-1]shl1; AREADLN (n); ans:=1; the    fori:=1  toN Do +   ifbo[i]=0  Thenans:= (ANS*QQ (i))MoDmo; - writeln (ans); $ End.

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BZOJ2734[HNOI2012] Collection of selected