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).
#include <bits/stdc++.h>
using namespace std;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long n, i, c = 0, b = LLONG_MIN, r, l;
  cin >> n;
  vector<long long> a(n), w(n);
  for (i = 0; i < n; i++) cin >> a[i];
  for (i = 0; i < n;) {
    r = l = i;
    while (l && a[l - 1] % a[i] == 0) l--;
    while (r < n - 1 && a[r + 1] % a[i] == 0) r++;
    i = r + 1;
    r -= l;
    if (r > b) c = 0, b = r;
    if (r == b) w[c++] = l + 1;
  }
  cout << c << " " << b << "\n";
  for (i = 0; i < c; i++) cout << w[i] << " ";
  cout << "\n";
  return 0;
}
