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
 */
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);
        ProblemDPairOfNumbers solver = new ProblemDPairOfNumbers();
        solver.solve(1, in, out);
        out.close();
    }

    static class ProblemDPairOfNumbers {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int[] a = new int[n + 1];
            for (int i = 1; i <= n; ++i) a[i] = in.nextInt();
            ProblemDPairOfNumbers.RMQ table = new ProblemDPairOfNumbers.RMQ(n, a);
            int low = 0;
            int high = n - 1;
            while (low <= high) {
                int mid = low + high >> 1;
                boolean possible = false;
                for (int i = mid + 1; i <= n; ++i) {
//                int min = tree.queryMin(1, i - mid, i);
                    int min = table.queryMin(i - mid, i);
                    int gcd = table.queryGcd(i - mid, i);
                    if (min == gcd) {
                        possible = true;
                        break;
                    }
                }
                if (possible) {
                    low = mid + 1;
                } else {
                    high = mid - 1;
                }
            }
            int mid = high;
            ArrayList<Integer> occ = new ArrayList<>(n);
            for (int i = mid + 1; i <= n; ++i) {
                int min = table.queryMin(i - mid, i);
                int gcd = table.queryGcd(i - mid, i);
                if (min == gcd) {
                    occ.add(i - mid);
                }
            }
            out.println(occ.size() + " " + mid);
            for (int i : occ) out.print(i + " ");
        }

        static class RMQ {
            int[] vs;
            int[][] minLift;
            int[][] gcdLift;

            int gcd(int x, int y) {
                return y == 0 ? x : gcd(y, x % y);
            }

            public RMQ(int n, int[] vs) {
                this.vs = vs;
                int maxlog = Integer.numberOfTrailingZeros(Integer.highestOneBit(n)) + 2;
                minLift = new int[maxlog][n + 1];
                gcdLift = new int[maxlog][n + 1];
                for (int i = 1; i <= n; i++)
                    minLift[0][i] = gcdLift[0][i] = vs[i];
                int lastRange = 1;
                for (int lg = 1; lg < maxlog; lg++) {
                    for (int i = 1; i <= n; i++) {
                        minLift[lg][i] = Math.min(minLift[lg - 1][i], minLift[lg - 1][Math.min(i + lastRange, n)]);
                        gcdLift[lg][i] = gcd(gcdLift[lg - 1][i], gcdLift[lg - 1][Math.min(i + lastRange, n)]);
                    }
                    lastRange *= 2;
                }
            }

            public int queryMin(int low, int hi) {
                int range = hi - low + 1;
                int exp = Integer.highestOneBit(range);
                int lg = Integer.numberOfTrailingZeros(exp);
                return Math.min(minLift[lg][low], minLift[lg][hi - exp + 1]);
            }

            public int queryGcd(int low, int hi) {
                int range = hi - low + 1;
                int exp = Integer.highestOneBit(range);
                int lg = Integer.numberOfTrailingZeros(exp);
                return gcd(gcdLift[lg][low], gcdLift[lg][hi - exp + 1]);
            }

        }

    }

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

    }
}

