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).
n = int(input()) + 1
t = [1] + list(map(int, input().split())) + [1]
p = [True] * n
s, q = 0, list(range(1, n))
for i in range(1, n):
    if p[i]:
        a = b = i
        d = t[i]
        if d == 1: 
            s, q = n - 2, [1]
            break
        while t[a - 1] % d == 0: a -= 1
        while t[b + 1] % d == 0:
            b += 1
            p[b] = False
        d = b - a
        if d > s: s, q = d, [a]
        elif d == s != 0: q.append(a)
print(len(q), s)
print(' '.join(map(str, q)))