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).
import sys
range = xrange
input = raw_input
from future_builtins import ascii, filter, hex, map, oct, zip

n = int(input())

A = [int(x) for x in input().split()]

explored = [0]*n
intervals = []
for i in range(n):
    if explored[i]:continue
    
    a = A[i]
    l = i
    while l>0 and A[l-1]%a==0:
        l -= 1

    r = i
    while r+1<n and A[r+1]%a==0:
        r += 1
    
    for i in range(l,r+1):
        if A[i]==a:
            explored[i] = 1
    intervals.append((l,r))

besta = max(r-l for l,r in intervals)
winners = set(l for l,r in intervals if r-l == besta)

print len(winners),besta

print ' '.join(str(l+1) for l in sorted(winners))
