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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Abhas Jain
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DPairOfNumbers solver = new DPairOfNumbers();
        solver.solve(1, in, out);
        out.close();
    }

    static class DPairOfNumbers {
        int[][] st_min;
        int[][] st_gcd;
        int n;
        int[] log;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            n = in.ni();
            int[] ar = new int[n];
            log = new int[n + 2];
            log[1] = 0;
            for (int i = 2; i <= n + 1; ++i) {
                log[i] = log[i / 2] + 1;
            }
            for (int i = 0; i < n; ++i) ar[i] = in.ni();
            st_min = new int[n][30];
            st_gcd = new int[n][30];
            for (int i = 0; i < n; ++i) {
                st_min[i][0] = ar[i];
                st_gcd[i][0] = ar[i];
            }
            for (int j = 1; j < 30; ++j) {
                for (int i = 0; i + (1 << j) <= n; ++i) {
                    st_min[i][j] = Math.min(st_min[i][j - 1], st_min[i + (1 << (j - 1))][j - 1]);
                    st_gcd[i][j] = maths.gcd(st_gcd[i][j - 1], st_gcd[i + (1 << (j - 1))][j - 1]);
                }
            }
            int lo = 1;
            int hi = n;
            //out.println(check(5));
            while (lo <= hi) {
                int mid = (lo + hi) / 2;
                if (check(mid)) lo = mid + 1;
                else hi = mid - 1;
            }
            int len = lo - 1;
            ArrayList<Integer> arr = new ArrayList<>();
            int min = -1, gcd = -1;
            int j = log[len];
            for (int i = 0; i + len - 1 < n; ++i) {
                int l = i;
                int r = i + len - 1;
                gcd = maths.gcd(st_gcd[l][j], st_gcd[r - (1 << (j)) + 1][j]);
                min = Math.min(st_min[l][j], st_min[r - (1 << (j)) + 1][j]);
                if (gcd == min) arr.add(i);
            }
            out.println(arr.size() + " " + (len - 1));
            for (int jj : arr) out.print((jj + 1) + " ");
        }

        public boolean check(int len) {
            int gcd = -1;
            int min = -1;
            int j = log[len];
            for (int i = 0; i + len - 1 < n; ++i) {
                int l = i;
                int r = i + len - 1;
                gcd = maths.gcd(st_gcd[l][j], st_gcd[r - (1 << (j)) + 1][j]);
                min = Math.min(st_min[l][j], st_min[r - (1 << (j)) + 1][j]);
                if (gcd == min) return true;
            }
            return false;
        }

    }

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

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int ni() {
            return Integer.parseInt(next());
        }

    }
}

