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.util.*;
public class Maximus {
static int GCD(int a,int b){
	if(b==0)return a;
	return GCD(b,a%b);
}	
public static void main(String [] args){
	Scanner in=new Scanner(System.in);
	int n=in.nextInt();
	int array[]=new int[n];
	for(int i=0;i<n;i++)array[i]=in.nextInt();
	int logn=(int)(Math.log(n)/Math.log(2)) + 1;
	int gcd[][]=new int[n][logn];
	int min[][]=new int[n][logn];
	for(int i=0;i<n;i++){
	min[i][0]=array[i];
	gcd[i][0]=array[i];
	}
	for(int j=1;(1<<j)<=n;j++){
		for(int i=0;i+(1<<j)-1<n;i++){
			int maxI=Math.max(gcd[i][j-1],gcd[i+(1<<(j-1))][j-1]);
			int minI=Math.min(gcd[i][j-1],gcd[i+(1<<(j-1))][j-1]);
			int Min=Math.min(min[i][j-1],min[i+(1<<(j-1))][j-1]);
			gcd[i][j]=GCD(maxI,minI);
			min[i][j]=Min;
		}
	}
	int low=0;
	int high=n+1;
	int fix=0;
	int cnt=0;
	int len=0;
	ArrayList<Integer>ans=new ArrayList<Integer>();
	while(low + 1 < high){
	int mid=(low+high)/2;
	len=(int)(Math.log(mid)/Math.log(2));
    boolean ifFound=false;
	for(int i=0;i<n-mid+1;i++){
	int j=i+mid-1;	
	int maxI=Math.max(gcd[i][len],gcd[j-(1<<len)+1][len]);
	int minI=Math.min(gcd[i][len],gcd[j-(1<<len)+1][len]);
	int Min=Math.min(min[i][len],min[j-(1<<len)+1][len]);
	int Gcd=GCD(maxI,minI);
	if(Gcd==Min){
	ifFound=true;break;
	}	
	}
	if(!ifFound)high=mid;
	else low=mid;
	//System.out.println(low+" "+mid+" "+high+" "+cnt+" "+fix);
	}
	len=(int)(Math.log(low)/Math.log(2));
	fix=low-1;
	for(int i=0;i<n-low+1;i++){
	int j=i+low-1;	
	int maxI=Math.max(gcd[i][len],gcd[j-(1<<len)+1][len]);
	int minI=Math.min(gcd[i][len],gcd[j-(1<<len)+1][len]);
	int Min=Math.min(min[i][len],min[j-(1<<len)+1][len]);
	int Gcd=GCD(maxI,minI);
	if(Gcd==Min){
	ans.add(i);cnt++;
	}	
	}
	System.out.println(cnt+" "+fix);
	for(int i=0;i<ans.size();i++)
		System.out.print((ans.get(i)+1) + " ");
}
}