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.util.*;
import java.io.*;

public class Main {

	BufferedReader in;
	StringTokenizer str = null;
	PrintWriter out;
	
	private String next() throws Exception{
		while (str == null || !str.hasMoreElements())
			str = new StringTokenizer(in.readLine());
		return str.nextToken();
	}
	
	private int nextInt() throws Exception{
		return Integer.parseInt(next());
	}
	
	private long nextLong() throws Exception{
		return Long.parseLong(next());
	}
	
	private double nextDouble() throws Exception{
		return Double.parseDouble(next());
	}
	
	int n;
	int []a;
	SparseTableMin minTree;
	SparseTableGcd gcdTree;

	// Random rnd;

	public void run() throws Exception{
		in =  new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(System.out);

		// rnd = new Random();

		n = nextInt();
		a = new int[n];
		for(int i=0;i<n;i++) a[i] = nextInt();

		minTree = new SparseTableMin(a);
		gcdTree = new SparseTableGcd(a);

		// for(int i=0;i<10;i++){
		// 	int l = rnd.nextInt(n);
		// 	int r = rnd.nextInt(n);

		// 	if (l > r) {
		// 		int t = l;
		// 		l = r;
		// 		r = t;
		// 	}

		// 	System.out.print(l + " " + r + " ");
		// 	System.out.println(gcdTree.gcd(l, r));
		// }

		int max = 0;
		Set<Integer> left = new HashSet<Integer>();

		for(int i=0;i<n;i++){
			int l = findLeft(0, i);
			int r = findRight(i, n-1);
			if (r - l > max) {
				max = r - l;
				left.clear();
				left.add(l + 1);
			}else if (r - l == max){
				left.add(l + 1);
			}
		}

		out.println(left.size() + " " + max);
		int []r = new int[left.size()];
		int yk = 0;
		for(int i : left) r[yk++] = i;
		Arrays.sort(r);
		for(int i : r)
			out.print(i + " ");
		out.println();
		out.close();
	}

	private int findLeft(int tl, int tr) {
		int l = tl - 1, r = tr + 1;
		while(r - l > 1) {
			int m = l + (r - l)/2;
			if (minTree.min(m, tr) == gcdTree.gcd(m, tr)) {
				r = m;
			}else {
				l = m;
			}
		}

		return r;
	}

	private int findRight(int tl, int tr) {
		int l = tl - 1, r = tr + 1;
		while(r - l > 1) {
			int m = l + (r - l)/2;
			if (minTree.min(tl, m) == gcdTree.gcd(tl, m)) {
				l = m;
			}else {
				r = m;
			}
		}

		return l;
	}

	static int log(int k) {
		int c = 0;
		while((1 << c) < k) c++;
		if ((1 << c) != k) c--;
		return c;
	}

	class SparseTableMin {
		int [][]m;
		int []a;
		public SparseTableMin(int []a) {
			this.a = a;
			int n = a.length;
			int log = log(n);
			m = new int[n][log+1];
			for(int i=0;i<n;i++) m[i][0] = i;
			for(int i=1;i<=log;i++){
				for(int j=0;j + (1<<i) <= n;j++){
					if (a[m[j][i-1]] < a[m[j + (1<<(i-1))][i-1]]) {
						m[j][i] = m[j][i-1];
					}else {
						m[j][i] = m[j + (1<<(i-1))][i-1];
					}
				}
			}
		}

		public int min(int l, int r) {
			// if (l == r) return m[l][0];
			int k = r - l + 1;
			k = log(k);

			return Math.min(a[m[l][k]], a[m[r - (1<<k) + 1][k]]);
		}
	}

	class SparseTableGcd {
		int [][]m;
		public SparseTableGcd(int []a) {
			int n = a.length;
			int log = log(n);
			m = new int[n][log+1];
			for(int i=0;i<n;i++) m[i][0] = a[i];
			for(int i=1;i<=log;i++){
				for(int j=0;j + (1 << i) <= n;j++){
					m[j][i] = _gcd(m[j][i-1], m[j + (1 << (i-1))][i-1]);
				}
			}
		}

		public int gcd(int l, int r) {
			// if (l == r) return m[l][0];
			int k = r - l + 1;
			k = log(k);

			return _gcd(m[l][k], m[r - (1 << k) + 1][k]);
		}

		private int _gcd(int a, int b) {
			return (b == 0) ? a : _gcd(b, a % b);
		}
	}
		
	public static void main(String[] args) throws Exception{
		new Main().run();
	}
}
