Problem: Snuke has a sequence p, which is a permutation of (0,1,2, ...,N-1). The i-th element (0-indexed) in p is p_i.

He can perform N-1 kinds of operations labeled 1,2,...,N-1 any number of times in any order. When the operation labeled k is executed, the procedure represented by the following code will be performed:


for(int i=k;i<N;i++)
swap(p[i],p[i-k]);


He would like to sort p in increasing order using between 0 and 10^{5} operations (inclusive). Show one such sequence of operations. It can be proved that there always exists such a sequence of operations under the constraints in this problem.

Constraints

* 2 \leq N \leq 200
* 0 \leq p_i \leq N-1
* p is a permutation of (0,1,2,...,N-1).

Input

Input is given from Standard Input in the following format:


N
p_0 p_1 ... p_{N-1}


Output

Let m be the number of operations in your solution. In the first line, print m. In the i-th of the following m lines, print the label of the i-th executed operation. The solution will be accepted if m is at most 10^5 and p is in increasing order after the execution of the m operations.

Examples

Input

5
4 2 0 1 3


Output

4
2
3
1
2


Input

9
1 0 4 3 5 6 2 8 7


Output

11
3
6
1
3
5
2
4
7
8
6
3

Solution (in CPP):

Solution:
#include <stdio.h>
 
void swap(int* a,int* b){
    int po=*a;
    *a=*b;
    *b=po;
}
 
int seiretu(int* p,int N){
    for(int i=0;i<N;i++)if(p[i]!=i)return 0;
    return 1;
}
 
int main(void){
    int N;
    int count=0;
    int po[114514];
    scanf("%d",&N);
    int p[N];
    for(int i=0;i<N;i++)scanf("%d",&p[i]);
    while(seiretu(p,N)==0){
        if(p[0]<p[N-1]&&!(p[0]==0&&p[N-1]==N-1)){po[count]=N-1;count++;swap(&p[0],&p[N-1]);}
        for(int i=0;i<N-1;i++)swap(&p[i],&p[i+1]);po[count]=1;count++;
    }
    printf("%d\n",count);
    for(int i=0;i<count;i++)printf("%d\n",po[i]);
    return 0;
}