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 n, j, sum, ans, a[300001], b[300001], l[300001], r[300001];
int main() {
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> a[i];
  for (int i = 1; i <= n; i++) {
    l[i] = i;
    while (a[l[i] - 1] % a[i] == 0 && l[i] > 1) {
      l[i] = l[l[i] - 1];
    }
  }
  for (int i = n; i > 0; i--) {
    r[i] = i;
    while (a[r[i] + 1] % a[i] == 0 && r[i] < n) {
      r[i] = r[r[i] + 1];
    }
  }
  for (int i = 1; i <= n; i++) {
    if (r[i] - l[i] >= ans) {
      if (r[i] - l[i] > ans) {
        ans = r[i] - l[i];
        sum = 1;
        b[1] = l[i];
      } else {
        if (b[sum] != l[i]) {
          sum++;
          b[sum] = l[i];
        }
      }
    }
  }
  cout << sum << ' ' << ans << endl;
  for (int i = 1; i <= sum; i++) cout << b[i] << ' ';
}
