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.awt.*;
import java.io.*;
import java.util.*;

public class Abc {
    public static void main(String[] args) {
        FastReader sc = new FastReader();
        n=sc.nextInt();
        arr=new int[n];
        for (int i=0;i<n;i++)arr[i]=sc.nextInt();
        st=new int[n][k];
        sparse();
        int l=1,r=n;
        int ans=-1;
        while (l<=r){
            int mid=l+(r-l)/2;
            if (found(mid)){
                ans=mid;
                l=mid+1;
            }else r=mid-1;
        }
        ArrayList<Integer> ls=new ArrayList<>();
        for (int i=0;i<=n-ans;i++){
            boolean zero=true;
            int min=min(i,i+ans-1);
            for (int j=i;j<=i+ans-1;j++){
                if(arr[j]%min!=0){
                    zero=false;
                    break;
                }
            }
            if (zero)ls.add(i);
        }
        ans--;
        StringBuilder sb=new StringBuilder();
        sb.append(ls.size()+" "+ans+"\n");
        for(int i=0;i<ls.size();i++){
            sb.append((ls.get(i)+1)+" ");
        }
        System.out.println(sb);
    }
    static boolean found(int len){
        for (int i=0;i<=n-len;i++){
            int min=min(i,i+len-1);
            boolean zero=true;
            for (int j=i;j<=i+len-1;j++){
                if (arr[j]%min!=0){
                    zero=false;
                    break;
                }
            }
            if (zero){
                return zero;
            }
        }
        return false;
    }
    /*

     */
    static int st[][];// st[n][k]
    static int arr[];
    static int log[];//floor(log(i) base 2)
    static int k=25; //choose k>=ceil(log(n)+1);
    static int n;// length of arr;
    static void sparse(){// pre_process in o(nlogn)
        for (int i=0;i<n;i++){
            st[i][0]=arr[i];
        }
        for (int j=1;j<k;j++){
            for (int i=0;i+(1<<(j-1))<n;i++){
                st[i][j]=Math.min(st[i][j-1],st[i+(1<<(j-1))][j-1]);
            }
        }
        log=new int[n+1];
        log[1]=0;
        for (int i=2;i<=n;i++){//floor(log(i) base 2)
            log[i]=log[i/2]+1;
        }
    }
    static int min(int l,int r){// O(1)
        int j=log[r-l+1];
        return Math.min(st[l][j],st[r-(1<<j)+1][j]);
    }
    static int sum(int l,int r){// O(logn)
        int sum=0;
        for (int j=k;j>=0;j--){
            if ((1<<j)<=(r-l+1)){
                sum+=st[l][j];
                l+=(1<<j);
            }
        }
        return sum;
    }
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}