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.io.PrintWriter;
import java.util.StringTokenizer;

public class D {
    FastScanner in;
    PrintWriter out;

    public void run() {
        try {
            in = new FastScanner(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
            solve();
            out.close();
        } catch (IOException e) {
            e.printStackTrace();
        }
    }

    public void solve() throws IOException {
        int n = in.nextInt();
        int [] a = new int[n];
        int [][] b = new int[n][2];
        for (int i=0; i<n; i++) {
            a[i] = in.nextInt();
        }
        int i = 0;
        int j = 0;
        int k = 0;
        int l = 0;
        int r = 0;
        while (i < n) {
            j = i;
            k = i;
            l = i;
            r = i;
            while (j >= 0 && a[j] % a[i] == 0) {
                l = j;
                j--;
            }
            while (k < n && a[k] % a[i] == 0) {
                r = k;
                k++;
            }
            b[i][0] = l;
            b[i][1] = r;
            i = k;
        }
        int maxLength = Integer.MIN_VALUE;
        int diff = 0;
        for (int m=0; m<n; m++) {
            diff = b[m][1] - b[m][0];
            if (diff > maxLength) {
                maxLength = diff;
            }
        }
        int counter = 0;
        StringBuilder sb = new StringBuilder();
        for (int m=0; m<n; m++) {
            diff = b[m][1] - b[m][0];
            if (diff == maxLength) {
                counter++;
                sb.append(b[m][0]+1);
                sb.append(' ');
            }
        }
        if (sb.length() > 0) {
            sb.deleteCharAt(sb.length()-1);
        }
        out.println(counter + " " + maxLength);
        out.println(sb);
    }

    class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        FastScanner(InputStreamReader in) {
            br = new BufferedReader(in);
        }

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

            return str;
        }

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

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

    public static void main(String[] arg) {
        D o = new D();
        o.run();
    }

}
