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 Main {
    
    private static final long MOD = 1000000007;
    
    public static void main(String[] args) throws Exception {
        Scanner scan = new Scanner(System.in);
        
        int n = scan.nextInt();
        int[] arr = new int[n];
        read(scan, arr);
        
        int[] left = new int[n];
        int[] right = new int[n];
        for (int i = 0; i < n; i++) {
            left[i] = right[i] = i;
        }
        for (int i = n - 1; i >= 0; ) {
            int index = i - 1;
            while (index >= 0 && arr[index] % arr[i] == 0) {
                index--;
            }
            left[i] = index + 1;
            i = index;
        }
        for (int i = 0; i < n; ) {
            int index = i + 1;
            while (index < n && arr[index] % arr[i] == 0) {
                // traps!!!!
                if (arr[index] == arr[i]) {
                    left[i] = Math.min(left[i], left[index]);
                }
                index++;
            }
            right[i] = index - 1;
            i = index;
        }
        
        int max = 0;
        for (int i = 0; i < n; i++) {
            max = Math.max(max, right[i] - left[i]);
        }
        
        ArrayList<Integer> leftList = new ArrayList<Integer>();
        
        for (int i = 0; i < n; i++) {
            int temp = right[i] - left[i];
            if (temp == max) {
                leftList.add(left[i] + 1);
                i = right[i];
            }
        }
        
        System.out.println(String.format("%d %d", leftList.size(), max));
        print(leftList.toArray());
        
        scan.close();
    }
    
    private static long pow(long base, long r) {
        if (r == 0) {
            return 1;
        }
        long half = pow(base, r / 2);
        long res = (half * half) % MOD;
        if (r % 2 != 0) {
            res = (res * base) % MOD;
        }
        return res;
    }
    
    private static void print(int... arr) {
        System.out.print(arr[0]);
        for (int i = 1; i < arr.length; i++) {
            System.out.print(" ");
            System.out.print(arr[i]);
        }
        System.out.println();
    }
    
    private static void print(long... arr) {
        System.out.print(arr[0]);
        for (int i = 1; i < arr.length; i++) {
            System.out.print(" ");
            System.out.print(arr[i]);
        }
        System.out.println();
    }
    
    private static <T> void print(T... arr) {
        System.out.print(arr[0]);
        for (int i = 1; i < arr.length; i++) {
            System.out.print(" ");
            System.out.print(arr[i]);
        }
        System.out.println();
    }
    
    private static void read(Scanner scan, int[]... arrs) {
        int len = arrs[0].length;
        for (int i = 0; i < len; i++) {
            for (int[] arr : arrs) {
                arr[i] = scan.nextInt();
            }
        }
    }
    
    private static void read(Scanner scan, long[]... arrs) {
        int len = arrs[0].length;
        for (int i = 0; i < len; i++) {
            for (long[] arr : arrs) {
                arr[i] = scan.nextLong();
            }
        }
    }
    
    private static void decreaseByOne(int[]... arrs) {
        for (int[] arr : arrs) {
            for (int i = 0; i < arr.length; i++) {
                arr[i] --;
            }
        }
    }
}
