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.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

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

    static int[] currMax;
    static int n;

    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        n = Integer.parseInt(br.readLine());

        StringTokenizer st = new StringTokenizer(br.readLine());
        int[] nums = new int[n];
        boolean isOne = false;
        for (int i = 0; i < n; i++) {
            nums[i] = Integer.parseInt(st.nextToken());
            isOne |= (nums[i] == 1);
        }
        
        if (isOne) {
            System.out.println(1 + " " + (n - 1));
            System.out.println(1);
        } else {
            int maxLength = getMaxLength(nums);
            String out = getAnswer(maxLength, nums);
            System.out.println(out);
        }
    }

    private static String getAnswer(int maxLength, int[] nums) {
        StringBuilder sb = new StringBuilder();
        int cnt = 0;
        for (int i = 0; i < n; i++)
            if (currMax[i] == maxLength) {
                cnt++;
                sb.append(" ").append(i - maxLength + 2);
            }

        return cnt + " " + Math.max(0, (maxLength - 1)) + "\n" + sb.substring(1);
    }

    private static int getMaxLength(int[] nums) {
        currMax = new int[n];

        int len, maxLen = 0, x = 1;
        for (int i = 0; i < n; i += x) {
            int a = 0, b = 0;
            for (a = i - 1; a >= 0; a--)
                if (gcd(nums[i], nums[a]) != nums[i]) {
                    a++;
                    break;
                }
            a = Math.max(a, 0);

            for (b = i + 1; b < n; b++)
                if (gcd(nums[i], nums[b]) != nums[i]) {
                    b--;
                    break;
                }
            b = Math.min(b, n - 1);

            len = (i - a) + (b - i) + 1;
            maxLen = Math.max(len, maxLen);
            currMax[b] = len;

            x = b - i + 1;
        }

        return maxLen;
    }
}