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.*;
import java.util.*;

import static java.lang.Integer.*;
import static java.lang.Math.*;

public class Problem359D {
    static BufferedReader in;
    static PrintWriter out;

    public static void main(String[] args) throws Exception {
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        new Problem359D().go();
        out.close();
    }

    void go() throws IOException {
        int n = parseInt(in.readLine());
        String[] inp = in.readLine().split("\\s+");
        Num[] seq = new Num[n];
        for (int i = 0; i < n; i++) {
            int val = parseInt(inp[i]);
            seq[i] = new Num(val, i);
        }
        LinkedHashSet<Integer> orderList = new LinkedHashSet<Integer>();
        Arrays.sort(seq, Num.ValueComparator);
        for (int i = 0; i < n; i++) {
            orderList.add(seq[i].id);
        }
        Arrays.sort(seq, Num.IdComparator);

        TreeSet<Integer> resList = new TreeSet<Integer>();
        int maxLen = 0;
        boolean[] done = new boolean[n];
        int countDone = 0;
        while (!orderList.isEmpty()) {
            Iterator<Integer> iter = orderList.iterator();
            int curId = iter.next();
            done[curId] = true;
            iter.remove();
            int startId = curId;
            int endId = curId;
            int curVal = seq[curId].val;
            // try left
            for (int i = curId - 1; i >= 0; i--) {
                if (done[i])
                    break;
                if (seq[i].val % curVal == 0) {
                    startId = i;
                    done[i] = true;
                    orderList.remove(i);
                } else {
                    break;
                }
            }
            // try right
            for (int i = curId + 1; i < n; i++) {
                if (done[i])
                    break;
                if (seq[i].val % curVal == 0) {
                    endId = i;
                    done[i] = true;
                    orderList.remove(i);
                } else {
                    break;
                }
            }
            int curLen = endId - startId + 1;
            countDone += curLen;
            if (curLen > maxLen) {
                maxLen = curLen;
                resList = new TreeSet<Integer>();
                resList.add(startId);
            } else if (curLen == maxLen) {
                resList.add(startId);
            }
            if (n - countDone < maxLen)
                break;
        }

        out.println(resList.size() + " " + (maxLen - 1));
        String sep = "";
        StringBuilder resStr = new StringBuilder("");
        for (int x : resList) {
            resStr.append(sep + (x + 1));
            sep = " ";
        }
        out.println(resStr);
    }

    static class Num {
        int val;
        int id;

        public Num(int val, int id) {
            this.val = val;
            this.id = id;
        }

        public static Comparator<Num> ValueComparator = new Comparator<Num>() {
            public int compare(Num a, Num b) {
                return a.val - b.val;
            }
        };

        public static Comparator<Num> IdComparator = new Comparator<Num>() {
            public int compare(Num a, Num b) {
                return a.id - b.id;
            }
        };

        @Override
        public String toString() {
            return "[id=" + id + ", val=" + val + "]";
        }
    }
}
