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 math
# import collections
# from itertools import permutations
# from itertools import combinations
# import sys
# sys.stdin = open('input.txt', 'r')
# sys.stdout = open('output.txt', 'w')


'''def is_prime(n):
    j=2
    while j*j<=n:
        if n%j==0:
            return 0
        j+=1
    return 1'''


'''def gcd(x, y):
    while(y):
        x, y = y, x % y
    return x'''

'''fact=[]
def factors(n) :
     
    i = 1
    while i <= math.sqrt(n):
         
        if (n % i == 0) :
             
            if (n / i == i) :
                fact.append(i)

            else :
    
                fact.append(i)
                fact.append(n//i)
        i = i + 1'''


def prob():
    
    n = int(input())
    n+=1
    # s=input()
    l=[1]
    l+=[int(x) for x in input().split()]
    l+=[1]
    # a,b = list(map(int , input().split()))

    p = [True]*n

    s=0

    q = [i for i in range(1,n)]

    for i in range(1,n):

        if p[i]:
            a=i
            b=i
            d=l[i]

            if d==1:
                s,q = n-2 , [1]
                break

            while l[a-1] % d == 0:
                a-=1

            while l[b+1] % d == 0:
                b+=1
                p[b]=False

            d = b-a

            if d>s:
                s,q = d,[a]
            elif d==s and s!=0:
                q.append(a)
        
    print(len(q) , s)
    print(*q)
    


t=1
# t=int(input())

for _ in range(0,t):
    prob()