Pair of Numbers
Description
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:
- there is integer j (l ≤ j ≤ r), such that all integers al, al + 1, ..., ar are divisible by aj;
- 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.
The first line contains integer n (1 ≤ n ≤ 3·105).
The second line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 106).
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.
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.
Samples
5
4 6 9 3 6
1 3
2
5
1 3 5 7 9
1 4
1
5
2 3 5 7 11
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).