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.BufferedOutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashSet;
import java.util.InputMismatchException;

public class Round209D {

	public static void solve() {
		int n = s.nextInt();
		int[] arr = s.nextIntArray(n);
		int[] pref_dp = new int[n];
		pref_dp[0] = 1;
		for(int i = 1; i < n; i++) {
			int prev = i - 1;
			int curr = arr[i];
			while(prev >= 0 && arr[prev] % curr == 0) {
				prev -= pref_dp[prev];
			}
			pref_dp[i] = i - prev;
		}
		int[] suff_dp = new int[n];
		suff_dp[n - 1] = 1;
		for(int i = n - 2; i >= 0; i--) {
			int next = i + 1;
			int curr = arr[i];
			while(next < n && arr[next] % curr == 0) {
				next += suff_dp[next];
			}
			suff_dp[i] = next - i;
		}
		int max = 1;
		HashSet<Integer> ans = new HashSet<Integer>();
		for(int i = 0; i < n; i++) {
			int curr = pref_dp[i] + suff_dp[i] - 1;
			if(max < curr) {
				ans.clear();
				max = curr;
				ans.add(i - pref_dp[i] + 1);
			}else if(max == curr){
				ans.add(i - pref_dp[i] + 1);
			}
		}
		Object[] helper = ans.toArray();
		Arrays.sort(helper);
		out.println(ans.size() + " " + (max - 1));
//		for(Integer x : ans) {
//			out.print(x + 1);
//			out.print(" ");
//		}
		for(int i = 0; i < helper.length; i++) {
			out.print((int)helper[i] + 1);
			out.print(" ");
		}
	}
		
	public static void main(String[] args) {
		new Thread(null, null, "Thread", 1 << 27) {
			public void run() {
				try {
					out = new PrintWriter(new BufferedOutputStream(System.out));
					s = new FastReader(System.in);
					solve();
					out.close();
				} catch (Exception e) {
					e.printStackTrace();
					System.exit(1);
				}
			}
		}.start();
	}

	public static PrintWriter out;
	public static FastReader s;

	public static class FastReader {

		private InputStream stream;
		private byte[] buf = new byte[4096];
		private int curChar, snumChars;

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

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

		public int nextInt() {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int number = 0;
			do {
				number *= 10;
				number += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return number * sgn;
		}

		public long nextLong() {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			long sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long number = 0;
			do {
				number *= 10L;
				number += (long) (c - '0');
				c = read();
			} while (!isSpaceChar(c));
			return number * sgn;
		}

		public int[] nextIntArray(int n) {
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = this.nextInt();
			}
			return arr;
		}

		public long[] nextLongArray(int n) {
			long[] arr = new long[n];
			for (int i = 0; i < n; i++) {
				arr[i] = this.nextLong();
			}
			return arr;
		}

		public String next() {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public String nextLine() {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndofLine(c));
			return res.toString();
		}

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

		public boolean isEndofLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}

	}

	
}
