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.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.Writer;
import java.util.Set;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.TreeSet;
import java.io.InputStream;

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

    static class TaskD {
        int n;
        int[] a;

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            a = in.readIntArray(n = in.readInt());
            SparseTable gcdTable = new SparseTable(this::gcd);
            Set<Integer> answers = new TreeSet<>();
            int answerLen = 0;
            for (int mid = 0; mid < n; mid++) {
                int l = -1;
                int r = mid;
                while (r - l > 1) {
                    int m = l + r >> 1;
                    if (gcdTable.get(m, mid) != a[mid]) {
                        l = m;
                    } else {
                        r = m;
                    }
                }
                int left = r;
                l = mid;
                r = n;
                while (r - l > 1) {
                    int m = l + r >> 1;
                    if (gcdTable.get(left, m) == a[mid]) {
                        l = m;
                    } else {
                        r = m;
                    }
                }
                int right = l;
                int len = right - left + 1;
                if (answerLen < len) {
                    answerLen = len;
                    answers.clear();
                }
                if (answerLen == len) {
                    answers.add(left + 1);
                }
            }
            out.printLine(answers.size(), answerLen - 1);
            out.print(answers.toArray());
        }

        int gcd(int a, int b) {
            return b == 0 ? a : gcd(b, a % b);
        }

        class SparseTable {
            int[] lenToLog;
            int[][] st;
            IntIntToIntFunction f;

            SparseTable(IntIntToIntFunction f) {
                this.f = f;
                lenToLog = new int[n + 1];
                for (int len = 1, log = 0; len < lenToLog.length; len++) {
                    if ((1 << (log + 1)) == len) {
                        log++;
                    }
                    lenToLog[len] = log;
                }
                st = new int[n][lenToLog[n] + 1];
                for (int i = n - 1; i >= 0; i--) {
                    st[i][0] = a[i];
                    for (int log = 1; i + (1 << log) <= n; log++) {
                        st[i][log] = f.value(st[i][log - 1], st[i + (1 << (log - 1))][log - 1]);
                    }
                }
            }

            int get(int l, int r) {
                int len = r - l + 1;
                int log = lenToLog[len];
                return f.value(st[l][log], st[r - (1 << log) + 1][log]);
            }

        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int[] readIntArray(int size) {
            int[] array = new int[size];
            for (int i = 0; i < size; i++) {
                array[i] = readInt();
            }
            return array;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int readInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

        public void printLine(Object... objects) {
            print(objects);
            writer.println();
        }

        public void close() {
            writer.close();
        }

    }

    static interface IntIntToIntFunction {
        public int value(int first, int second);

    }
}

