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()
from sys import *
lst=map(int,stdin.readline().split())

ans=[]
i=0
fv=-4
while i<n:
    l=i
    r=i
    while l and lst[l-1]%lst[i]==0:
        l=l-1
    while r<n-1 and lst[r+1]%lst[i]==0:
        r=r+1
    i=r+1
    if r-l>=fv:
        fv=r-l
        ans.append((r-l,l))

c=0
f=[]

for i in range(0,len(ans)):
    if ans[i][0]==fv:
        c=c+1
        f.append(ans[i][1]+1)

print c,fv
f.sort()
for i in f:
    stdout.write(str(i)+" ")