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.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Scanner;

public class _33_Pair_of_Numbers {

	public static void main(String[] args) {
		Scanner scn = new Scanner(System.in);
		int n = scn.nextInt();
		int[] arr = new int[n];
		logtable = new int[n + 1];
		for (int i = 2; i <= n; i++) {
			logtable[i] = logtable[i >> 1] + 1;
		}
		for (int i = 0; i < n; i++) {
			arr[i] = scn.nextInt();

		}
		
		sparsebuilt(arr, n, logtable);
		int l = 0;
		int r = n;
		int len = l;
		while (l<= r) {
			int v = l + (r - l) / 2;
			if(v==0){
				break;
			}
			if (ok(v, n)) {
				len=v;
				if(l==r){
					break;
				}
			     l=v+1;
			} else {
				r = v-1;
			}
			
		}
		
		ArrayList<Integer> ans = new ArrayList<>();
		if(len==0){
			System.out.println(n+" "+0);
			for (int i = 0; i  < n; i++) {
				System.out.print((i+1)+" ");
			}
		}else{
		for (int i = 0; i + len - 1 < n; i++) {
			if (query(i, i + len - 1)) {
				ans.add(i);
			}
		}
		System.out.println(ans.size()+" "+(len-1));
		for(int i=0;i<ans.size();i++){
			System.out.print((ans.get(i)+1)+" ");
		}}
	}

	static int[][] table;
	static int[][] gc;
	static int[] logtable;

	public static void sparsebuilt(int[] arr, int n, int[] logtable) {
		table = new int[n][logtable[n] + 1];
		gc = new int[n][logtable[n] + 1];
		for (int i = 0; i < n; i++) {
			table[i][0] = arr[i];
			gc[i][0] = arr[i];
		}

		for (int j = 1; ((1 << j) <= n); j++) {
			for (int i = 0; (i + (1 << (j - 1))) < n; i++) {
				table[i][j] = Math.min(table[i][j - 1], table[i + (1 << (j - 1))][j - 1]);
				gc[i][j] = gcd(gc[i][j - 1], gc[i + (1 << (j - 1))][j - 1]);
			}
		}
	}

	public static int gcd(int a, int b) {
		if (b == 0) {
			return a;
		}
		return gcd(b, a % b);
	}

	public static boolean query(int l, int r) {
		int j = logtable[r - l];

		int min = Math.min(table[l][j], table[r - (1 << j) + 1][j]);

		int gcl = gcd(gc[l][j], gc[r - (1 << j) + 1][j]);
		if (min == gcl) {
			return true;
		}
		return false;
	}

	public static boolean ok(int len, int n) {
		for (int i = 0; i < n; i++) {
			if (i + len - 1 < n) {
				if (query(i, i + len - 1)) {
					return true;
				}
			}
		}
		return false;
	}
}
