Simon has an array a1, a2, ..., an, consisting of n positive integers. Today Simon asked you to find a pair of integers l, r (1 ≤ l ≤ r ≤ n), such that the following conditions hold:

  1. there is integer j (l ≤ j ≤ r), such that all integers al, al + 1, ..., ar are divisible by aj; 
  2. value r - l takes the maximum value among all pairs for which condition 1 is true; 



Help Simon, find the required pair of numbers (l, r). If there are multiple required pairs find all of them.

Input

The first line contains integer n (1 ≤ n ≤ 3·105).

The second line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 106).

Output

Print two integers in the first line — the number of required pairs and the maximum value of r - l. On the following line print all l values from optimal pairs in increasing order.

Examples

Input

5
4 6 9 3 6


Output

1 3
2 


Input

5
1 3 5 7 9


Output

1 4
1 


Input

5
2 3 5 7 11


Output

5 0
1 2 3 4 5 

Note

In the first sample the pair of numbers is right, as numbers 6, 9, 3 are divisible by 3.

In the second sample all numbers are divisible by number 1.

In the third sample all numbers are prime, so conditions 1 and 2 are true only for pairs of numbers (1, 1), (2, 2), (3, 3), (4, 4), (5, 5).
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashSet;

public class NumberPairs2{

        public static void main(String[] argv) throws Exception{
            BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
            int n=Integer.parseInt(br.readLine().trim());
            String[] words=br.readLine().trim().split(" ");
            int[] a=new int[n+1];
            for(int i=0; i<n; i++){
                    a[i+1]=Integer.parseInt(words[i]);
            }
            int[] left=new int[n+1];
            left[1]=1;
            for(int i=2; i<=n; i++){
                    if(a[i]==a[i-1]){
                            left[i]=left[i-1];
                    }else{
                            left[i]=i;
                    }
            }
            int[] right=new int[n+1];
            right[n]=n;
            for(int i=n-1; i>=1; i--){
                    if(a[i]==a[i+1]){
                            right[i]=right[i+1];
                    }else{
                            right[i]=i;
                    }
            }
            int j, startPos, endPos;
            ArrayList<Pair> pairList=new ArrayList<Pair>(n);
            pairList.add(new Pair(0, 0));
            for(int i=1; i<=n; i++){
                    pairList.add(new Pair(i, 1));
            }
            int max=0;
            Pair curPair;
            for(int i=1; i<=n; i++){
                    //System.out.println(i+":"+a[i]);
                    startPos=i;
                    endPos=i;
                    j=startPos;
                    //System.out.println("before while j:"+j);
                    while(j>=1){
                        if(a[j]%a[i]==0){
                            curPair=pairList.get(j);
                            j=curPair.pos;
                            endPos=curPair.pos+curPair.len;
                            j--;
                        }else{
                            startPos=j+1;
                            break;
                        }
                    }
                    //System.out.println("after while j:"+j);
                    if(j<1){
                        startPos=1;
                    }
                    j=endPos;
                    while(j<=n){
                        if(a[j]%a[i]==0){
                            j=right[j];
                            j++;
                        }else{
                            endPos=j-1;
                            break;
                        }
                    }
                    if(j>n){
                        endPos=n;
                    }
                    //System.out.println(i+" "+startPos+","+endPos);
                    pairList.get(i).pos=startPos;
                    pairList.get(i).len=endPos-startPos;
                    if(endPos-startPos>max){
                            max=endPos-startPos;
                    }
            } 
            ArrayList<Pair> pairListRes=new ArrayList<Pair>();
            HashSet<Integer> posSet=new HashSet<Integer>();
            for(int i=1; i<pairList.size(); i++){
                    curPair=pairList.get(i);
                    if(curPair.len==max){
                        if(!posSet.contains(curPair.pos)){
                            pairListRes.add(curPair);
                            posSet.add(curPair.pos);
                        }
                    }
            } 
            Collections.sort(pairListRes, new PairPosComparator());
            System.out.println(pairListRes.size()+" "+max);
            for(int i=0; i<pairListRes.size(); i++){
                    System.out.print(pairListRes.get(i).pos+" ");
            }
            System.out.println();
        }
}
class Pair{
        int pos, len;
        public Pair(int pos, int len){
                this.pos=pos; this.len=len;
        }
}
class PairPosComparator implements Comparator<Pair>{
        public int compare(Pair p1, Pair p2){
                if(p1.pos>p2.pos)
                        return 1;
                else if(p1.pos<p2.pos)
                        return -1;
                else
                        return 0;
        }
}

