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 = input()
a = map(int, raw_input().split())

flag = [False for i in xrange(n)]
max_len = -1
ans = []

if min(a) == 1:
    print 1, n - 1
    print 1
    exit()

for i in xrange(n):
    if flag[i]: continue
    
    to_left = i - 1
    while to_left >= 0 and a[to_left] % a[i] == 0:
        to_left -= 1
        
    to_right = i + 1
    while to_right < n and a[to_right] % a[i] == 0:
        if a[to_right] == a[i]:
            flag[to_right] = True
        to_right += 1
    
    cur_len = to_right - to_left - 2
    #print i, cur_len
    if cur_len > max_len:
        max_len = cur_len
        ans = []
        ans.append(to_left + 1)
    elif cur_len == max_len:
        ans.append(to_left + 1)
        
print len(ans), max_len
ans = sorted(ans)
for i in xrange(len(ans)):
    if i == len(ans) - 1:
        print ans[i] + 1
    else:
        print ans[i] + 1,
