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).

from sys import stdin, stdout
read_ints = lambda: map(int, raw_input().split())
read_floats = lambda: map(float, raw_input().split())

def main():
    n = read_ints()[0]
    arr = read_ints()
    r_len = [0 for i in range(n)]
    l_len = [0 for i in range(n)]
    left_d = 0
    for i in range(1, n):
        if arr[i] % arr[left_d] == 0:
            r_len[left_d] += 1
        else:
            if r_len[left_d] != 0:
                for j in range(left_d + 1, i):
                    if arr[j] == arr[left_d]:
                        r_len[j] = r_len[left_d] - (j-left_d)
            left_d = i

    if r_len[left_d] != 0:
        for j in range(left_d + 1, n):
            if arr[j] == arr[left_d]:
                r_len[j] = r_len[left_d] - (j-left_d)

    right_d = n - 1
    for i in range(n - 2, -1, -1):
        if arr[i] % arr[right_d] == 0:
            l_len[right_d] += 1
        else:
            if l_len[right_d] != 0:
                for j in range(i+1, right_d):
                    if arr[j] == arr[right_d]:
                        l_len[j] = l_len[right_d] - (right_d - j)
            right_d = i
    if l_len[right_d] != 0:
        for j in range(0, right_d):
            if arr[j] == arr[right_d]:
                l_len[j] = l_len[right_d] - (right_d - j)

    total_len = [l_len[i] + r_len[i] + 1 for i in range(n)]
    max_len = max(total_len)
    max_nrr = list(set([ i - l_len[i] + 1 for i in range(n) if total_len[i] == max_len]))
    max_nrr.sort()
    max_len_cnt = len(max_nrr)

    print max_len_cnt, max_len - 1
    print ' '.join([ str(i) for i in max_nrr])


if __name__ == '__main__':
    main()
